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I've seen some good advice on welders, accessories, and processes.  Thought I would write you a short book on how to weld and use that gear.

What welding is:  
-You have received recommendations for 120v and 220v welders, MIG (GMAW) and Stick (SMAW), and even torches.  All of these do the same thing in different ways: they melt metal.  If you get a 120v welder that runs on your home service, it will not draw as much power as a 220v welder.  In this case, the voltage and amperage is how deep the melting can happen in the metal.

-To better explain:  If you are welding something thin such as 1/16" or 1/8" metal sheets, you want a low amperage so that the weld process doesn't just burn up your metal.  If the amperage is too high, it is like trying to light a candle with a flame thrower.  On the other hand, if you have a 1/2" thick piece of steel and you use a low amperage then the weld won't penetrate very deep into the metal.  You will end up with a surface weld and the joint will be weak.  If the amperage is too low, it is like trying to use a candle to heat your house.

I will buy a 120 v welder (I'm old enough to want to call that 110, btw).  I don't have 220 outside or in the garage at this point, and won't be putting it there any time soon, unfortunately.
Nothing wrong with that.  A smaller welder will just need to make a lot more passes to weld bigger stuff.

What kind of welder do you need?    
-This is so subjective.  Here are some things that you should think about.  
1. What is the thickest piece of metal that you might want to weld?  What is the thinnest?  What type of metal is it (steel, aluminum, nickel/chrome, etc)?
2. What is the duty cycle?  Duty cycle is how much it can run before it needs to rest and cool down.  A 60% duty cycle means it can run continuously for 6 minutes and needs to rest for 4.  That's a LOT of welding for a homeowner.
3. How good are the windings?  Miller and Lincoln are industry standards.  They have heavier windings and electrical components to provide better current output.  Cheap welders from Harbor Freight will work fine at home, but they are cheap because the important parts are cheap.

Good thoughts, and far better than a "just don't buy Harbor Freight because it's Harbor Freight."  

Thickness:  I don't know.  Type?  Whatever I encounter.   I know I will have significant limitations with my first welder.  I know I can't weld thick things probably.  Beyond that, I don't know. I want to fix things that break, like lawn furniture.  Some of that is powder coated metal.  Some of it is painted (I think) steel and is just plain old--my dad gave it to me, which is why I want to fix it and not toss it. Some is very thin metal (might be aluminum but I think it's more likely steel lawn chairs that belonged to my grandparents.  I don't even know if I CAN fix any of this.  But every year I stare at it and go, "Dammit I wanna FIX that.  I want the capability to fix it myself."  

Duty cycle:  I won't need to weld long before I take a break. And I won't be moving straight on to the next joint.  I'll be slow.  
If most of your stuff is thin, MIG will help.  Stick can do sort of thin, but you need to weld at low current, it's easy to burn through, and you may stick the rod to the piece more times than you want.

How to use these different machines:

STICK (SMAW)  
- You can do almost every type of welding with a stick welder.  Use your smart phone and download the Miller weld app.  You input your type of steel and size of electrode (welding rod) and it will tell you what amperage range to use for that weld.  If 90% of your welding is just mild steel, a stick welder will meet your needs.  
- The stick welder has two leads.  You can plug the electrode (holds rod) into either the positive or negative, and the ground in the other.  Each of these has pros and cons.  Usually DCEP (DC current, electrode positive) has the most penetration.  DCEN (DC current, electrode negative) has the least penetration.  So to work on your farm plow you will probably use DCEP with a higher current, and to work on your thin sheet metal you will probably use DCEN with a lower current.

This is really good.  Simple.  Understandable.  And is a brilliant help when thinking about settings.  Thank you.  I remember learning some of this in school, but so long ago I have no detail memory.

The only welding I have ever done was with a stick, and that was many, many years ago. I won't be buying a stick welder, so is the app still good if I have a small, inexpensive wire welder? That's almost certainly what I'll end up with  starting out.  The reason is that I need to see how much of this I will realistically do.  If I end up needing it a bunch, I'll upgrade, but unlike most things I buy (I normally will go for the best quality I can get with my resources), I don't want to tie up money I can use for other things, only to have it just sitting there--not for this.  It doesn't make sense for me or our household to have a bunch of money (I know that's a relative term) in a piece of equipment I end up not  using for five or six years after I do a few projects that are irritating me because they're broken.   However, I really love the idea of having the power to stick two pieces of metal together with enough skill that the weld will function.  
Yes, the app is good for Stick, MIG, and TIG processes.

MIG (GMAW)  
-  MIG is a happy marriage between Stick and TIG.  With the stick welder, the welding rod is coated in a flux that burns to keep out oxygen.  With a flux core wire you get the same thing, but the flux is on the inside.

Wait...so...it's not flux coated wire, but it's wire-coated flux????  I had not gathered that from the learning I've done thus far.  It makes sense.  "Flux CORE" but I had just assumed that the core was the wire, like the rods I used to use.

Flux core MIG and Stick welding both have slag (the flux and impurities that coat the outside of the weld bead and have to be chipped away).  They also pop and splatter more, especially if the flux has absorbed moisture or the weld area is not prepped properly.  
- The benefits of flux core MIG are that you don't have to keep swapping sticks as they burn down, and you always keep the same distance from your weld since the wire is feeding itself up to your bead.

First, I did not realize that flux core was ALSO considered MIG, and that seems to be how you're speaking of it.  So I may have a hole in my terminology.  A lot of the sites where I've been reading have (I understood) considered flux core separate and called "MIG" the kind with the gas, and spoke of it as "Flux Core as opposed to MIG.  So I may speak of it wrong here, and if so, you'll understand my point of reference. ...So...
boostinjdm is right.  Usually MIG is used generically for a machine that feeds wire through the electrode cable when you press the trigger on the torch.  The different processes are actually different technically, so you need to read the specs on whatever machine you are looking at to see if it does what you want.

In the reading I've done, it seemed clear that one of the main benefits of flux core is that there is no gas, ONLY IF/BECAUSE if you're going to be welding outside, with no way to control the wind, that gas MIG may put you at a disadvantage.  This is the main reason I have been considering a flux core welder (cost is another reason--the little starter welders are stupid cheap, which is very appealing for someone wanting to try out a new skill and although I understand some people would be discouraged by splatter, I'm not going to be discouraged as long as I know it's coming as part of the process and that I will have to deal with it.)  I will ALWAYS be outside in the driveway, and it is nearly ALWAYS windy here where I live.  I can see myself getting very frustrated by trying to set up wind shields and having the wind whip around it and ruin what I'm doing, knock it over, basically be a pain in the butt and make me cuss a lot.  Once I read that on two or three sites, I kind of went, "okay flux core is the way I should go."  I am open to your thoughts on this, and since I've only been looking, and haven't bought anything yet, I have time to consider all input.
That's a strong wind!  Yes wind is bad when you're welding.  The gas comes out of a cup on your torch.  The cups come in different sizes, based on how much flow you need.  If you use flux core, no cup to worry about and no flow.  If you use gas, there will be other factors to getting a good flow of shield gas.  It's not hard, and I am sure you can find and print all the charts to tell you what sizes and settings to use.

-  If you want a clean weld, or want to do fine work on something like aluminum, you want a solid wire, gas weld setup.  

It seems that this is true for thin steel like auto bodies as well...is that correct?  In my reading, all the folks doing that kind of work are using the gas wire welders, and the guy who installed my exhaust system had a gas setup for his MIG welder. (Millermatic I think--with a big tank also on the cart.  I considered staging a diversion and running away with his welding cart.)  I don't know that I would ever get to the point that I would weld on an auto body, but the idea is intriguing to me.  I think at that point I would be investing in a whole bunch of stuff, and a new welder would be small beans.
My opinion is that most professionals use gas because it looks better and has less post-weld cleanup.  We use a flux core welder at the blacksmith shop and I can lay a bead on pretty thin stuff.  Any weld process is going to heat your project up.  The biggest challenge with welding thin stuff is controlling the heat.  You may lay a bunch of short beads and let it cool between them.  This is one place where your experience will build up and guide you.  If you try to just weld any project in one sitting it will go poorly.  Even a big project needs heat control.

By the way, I highly recommend getting a cart for all this stuff.  You won't regret it.

Not all MIG welders can be set up to flow a shield gas.  Since this process uses a gas to keep oxygen out (instead of burning flux) it is MUCH cleaner and without all the popping, splatter, and slag of the first two processes.  Some things like aluminum need this in order to work.  In addition, the REALLY thin wire that can be used with the gas may need a spool gun to use.  
-  Most MIG welders put a wire spool inside the machine and feed the fire through the cable to the torch.  This is fine for both flux core and solid wire, as long as it's thick enough to be pushed.  The really thin wires tend to bend and jam when pushed through the line, which is where the spool gun comes in.  All this does is move the wire spool out to your torch handle, which makes the distance to push MUCH shorter.  Usually you see this setup for welding really thin aluminum.

Okay good to know about the thin wire.  Will most welders (even the low end ones) allow the use of a spool gun INSTEAD of the feed through the cable?
You just need to look at the specs for whatever model you are looking at.  They should specify whether or not a spool gun is compatible.

- The quality of weld coming out of a solid wire, shield gas MIG is just as good as any TIG weld I can do.  For the money and versatility this is the type of welder I recommend you look at for your general use.

TIG  
- TIG is a two handed process.  You have an electrode that fits in the torch, and a shield gas that flows around it.  When you strike your arc, you feed the filler metal into the puddle using your other hand.  This is a very precise way to weld, which is why it is considered the top level (and hardest).  Honestly, if you can control C.L.A.M.S. in any weld process, you can weld with any of these just fine.  TIG just takes practice.  Since you say you aren't that experienced, I won't dive into more about this process unless you really want to know.

I am interested because I'm curious by nature, but I won't be getting that.  At least not in the near future. So no need for you to put the time into details.  

How to weld:

Step one: Weld prep  
-  You need to be sure that you grind, sand, and clean the weld effected area very well.  This means getting bare, clean metal at least one inch from the area you will be running your weld bead.  No rust, paint, dirt, etc.  This crap will get drawn into your weld, which weakens it.  Probably not enough for you to worry about in your hobby shop, but the Navy Hull Techs that did the Non-Destructive testing on our pipes and other welds were relentless.  The general process is to use your angle grinder to get the big stuff off, then emery cloth to fine clean the area, then wipe down with acetone and let air dry.  (Acetone evaporates quickly and helps remove any moisture).

Maybe a stupid question...Is acetone better than alcohol for this?  We used alcohol for this when I worked in TV production, but we were working with electronics.  That's my only experience with using a liquid to dissipate moisture, and I've used it for this ever since.
I don't really know the merits of alcohol vs acetone.  Both displace moisture out of the pores of the metal, and both evaporate quickly.  I think that whatever works is fine.  The end result needs to be clean metal.

Also...Any thoughts you have on the best attachments for the angle grinder would be really useful.  I know that's not specifically about welding, but I just bought my first angle grinder, and looked at all the available attachments, but have had no time to actually do anything with it.  I was a little overwhelmed by the number of things you can buy for it.  For general cleanup of the surface pre-weld, then the removal of slag and/or grinding/smoothing after the weld if necessary, I'm happy to hear what you use most often.  One of the folks here said he usually keeps two plugged in--one for brushes and one for grinding, just so he doesn't have to keep changing out the attachment.  That seemed like a good idea..
I personally like the sanding discs for my angle grinder.  I buy the discs that have a threaded insert because they are super easy to swap (no tool needed).  I also buy grinding wheels and cutting wheels for it.  A stiff wire wheel would work better for removing that powder coating you mentioned.  I say buy one of each and try them out.  You'll develop your own preference.  (By the way, I also use those sanding discs to sharpen my mower blades.  They work great for that.  
https://www.grainger.com/category/flap-discs/sanding-discs-and-kits/abrasives/ecatalog/N-10lp?adgrpID=1372925171&kwdID=+Sanding++Discs&s_kwcid=AL%212966%2110%218950921298%2162045476571

Step two: Get the tech sheet out.  
-  No matter what you are welding, there is a good welding rod/filler metal, and a good current to use.  Go to your Miller welding app or whatever your favorite app is and figure it out.  For example: If I am welding mild steel with 1/8" weld rod, Miller recommends 80-130 amps.  If I am welding up 1/4" metal with a solid core MIG, they recommend a 0.035" wire with a feed rate of 360-380 inch per minute,  either CO2 or Argon/CO2 mix for shield gas, and 180-190 amps.

Another stupid question...I don't know how steel is designated other than thickness.  I understand mild steel is relatively low in carbon.  But how do I know what's in front of me when I go to fix something?  I can probably figure out whether it's steel or not, as opposed to aluminum or cast iron or some other metal.  But what kind?  Would I automatically assume mild steel for most things in the home or shop?
Yes, most steel you see is going to be mild carbon steel.  Mild carbon steel, high carbon steel (also called spring steel), and cast iron are fairly common.  Most of the time you can take your grinder to it and look at how many sparks are thrown off.  A huge shower of sparks is probably mild carbon.  No sparks (or very few) is probably cast iron.  Somewhere in the middle is probably spring steel.  The biggest concern is heat control for spring steel and cast iron.  You want to heat up and cool down slowly.  The higher carbon content makes the steel stronger, but it also makes it more brittle.  If you quench the steel after a high heat, it has a higher tendency to break.  There should be plenty of info on this on the internet.  Look up things like "tempering spring steel," "tempering knife blade," or "steel hardness factor."  Once you start to learn about metallurgy, you know you are in DEEP!

Step 3: Weld  
-  If you can remember and control C.L.A.M.S. you will have a perfect weld every time.
Current:  The current is set at whatever you prefer, within the recommended range.  If you are stick welding and the current is too low, your rod will just stick to your project without arcing and you will get frustrated.  If current is too high, you will burn right through your project if you are not careful.  
Length of Arc:  You want the arc between the electrode and the project to be as small as possible.  If it's too close with stick, the stick will just attach to the project and you have to stop, break it off, grind it out, and start over.  If it's too close with TIG, you will get metal on your electrode and have to go to the grinder to fix the angle (I know, we didn't get into TIG, just know that it's a little more involved)  With any of the processes, if you are too far away it will let oxygen get drawn into the weld which causes porosity, popping, and splattering.  With Stick, you have to move the rod in, towards the weld the whole time.  With MIG and TIG, you hold the torch at the same distance from the project the whole time.
Angle:  You almost always want to add metal into the leading edge of the puddle.  That means that you want to hold the stick so that it points back towards the weld (roughly 45 degree angle for most applications.  You want to point MIG like this too, but I don't have quite as much angle.  TIG, you point from the back because you add the metal with your other hand from the front of the puddle.  One way to remember this is "Drag a stick" and I usually add "Push TIG."  That's the angle that the torch is to the weld, and you also have to control the angle to the project.  If you are welding two plates that make a 90 degree corner, you want to split the difference and hold at a 45 degree angle to the joint.  Think of it like this:  The torch is shooting electricity at your joint.  If you point it more towards one side, then the weld is going to go more towards that side.  If you want both pieces to weld together equally, then point it at both equally.  I realize this may sound confusing the way I wrote it, but once you weld it will make total sense.
Manipulation:  You need to work your weld puddle around.  That little puddle is your bead.  You might make some little movements side to side as you weld to make sure you are getting even penetration and forming a nice bead.
Speed:  If you strike an arc and hold the electrode in one place, it will continue to burn metal until you stop.  If you strike an arc and take off like a jackrabbit, it will only lay metal down as fast as it can burn.  You need to watch your puddle and move at whatever speed gets good penetration AND lays down a nice bead.

Step four: Evaluate your weld  
-You can look online for pictures of good welds and bad. You want a nice even bead, with even rings and good penetration. A good bead looks a little like a roll of dimes laid on its side and pushed over. A bad weld bead has undercut, roll-over, porosity, or is uneven. Just google those terms and you can see what they are.

I remember the row of dimes, and I got decent at making it look like that.  The tighter, the more even,  and thinner the dimes, the better, sort of.  But when I see wire welding demonstrated online, often the dimes look isn't as pronounced as I remember for stick welding.  Maybe they're just better welders than my instructors were....?
Definitely a C.L.A.M.S. and skill level variable.  

If you have any questions, put them out and we can try to answer them.  Hope this helps.  It's a very basic crash course in welding.


One more thought:  Cutting torches.  
- Oxy acetylene is the standard.  It is hot enough to cut (with a cutting tip), and you can also weld and braze with it (with the brazing tip).  If you use it to weld, you are doing the same thing as the other weld processes.  You just use gas and flame to melt the metal instead of electricity.  Hold the flame over your weld area, and when you get a little molten puddle to form you start adding your filler metal (to the leading edge of the puddle.)
-  Using a propane torch will cut also, but may not get hot enough to weld very much.  Petrogen torches also work for cutting, but are more difficult for most people to use (they use white gas that you have to keep pumping up to maintain pressure, and you have to heat the tip before you can use it).
-  If you are going to invest in a torch setup, I recommend getting the bigger bottles and a cart to haul them around on.  Invest in Victor gages and torches.  I bought a little pony bottle setup and regret it.  Runs out of gas WAY too quick.  I find myself running over to my dad's to use his bigger setup instead of constantly filling my bottles.

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I think that do hickey on the trailer is a rock screen.   Pick up a bucket of earth, dump on screen, dirt goes through, rocks slide to the outside.

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OP hope you dont mind if I ask for help also.



I have wanted to play with/learn to weld for several years .. haven't touched a welder in 25 years and even then it was arc in shop class in high school, and I doubt I remember any of it.  Similar to OP, around the house/shop use, trailer/camper work, stuff, etc.



I under stand buy once, cry once but also some times its baby steps.  



That said, hoping for some thoughts on either of these on my local CL



http://salem.craigslist.org/tls/5874360865.html



http://salem.craigslist.org/for/5876486048.html



TIA

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Completely   agree on the shortfalls of flux core welding, they do look less appealing than a more industrial welder and shielding gas.





But like I've said in this thread before, flux core gets the job done. I weld up to 1/4" with my little 120VAC flux core wire welder (rated up to like 1/8" or something). Just takes practice and a little different technique to get better grab. Still not as good as a weld as a bigger welder, and I don't use it on that thick of steel where safety is a factor, but I make tractor implements with it and nothing has ever broke on me.





The 2 main HUGE advantages for me with the flux core is cost (no argon bottle to buy and fill, welder is cheaper to start with), and operates in windy conditions just the same (I have no shop, everything is done outside). Yes, the flux core wire is more expensive, but if you buy the bigger roll (25 pound IIRC) it isn't that bad. I build a fair amount of stuff and a roll lasts me well over a year.





My little vid of my setup

https://www.youtube.com/watch?v=SAqaIIhU1Tg

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You    only need 1 size of flux core wire. Don't tell anybody, but I have wire that is 3 years old I am still using.
We some welding rod that was gov't over-stock. It was from either Korea or Vietnam over-stock. Grandpa picked up a pallet for stupid cheap. STILL use that today as well, although it isn't as good as brand new high quality rods it does weld better than the cheap rods you get from HF and such.