I am working on my first AR-15 build and need some help.  I have already purchased a stripped Aero lower receiver and couple of 30 round Magpul magazines.  I now have about $450 to spend on my build and am looking for input on what to buy next.  The rifle will be used for plinking, possibly deer hunting (my 11 year old son) and as a SHTF  rifle.  I will be shooting it mainly but so will my son, daughter and wife (so it needs to be adjustable).  I don't want to spend a fortune (I'm not some super serious, competitive shooter) but I want something that will be moderately accurate and something that is durable and reliable.   So what should I buy next?  Should I look into buying a completed upper?  If so, is Palmetto State Armory a good source or is there somewhere better?  I'm totally new to the AR world so try not to be too hard on me.  Thanks!

By the sounds of what you're saying, a complete Upper from Palmetto State would work just fine for you. They're inexpensive enough it will perform for what you're looking for. But if you're thinking of using it for deer hunting... you just complicated your situation. In my opinion there's other calibers that would be better Suited for taking Whitetail. In time you can always pick up a new upper to slap on the lower, after you've done more research

Good starter upper

Thanks!  I understand about the deer hunting.  I know a .223 is a bit light for deer.  He is only 10 (will be 11 for next year's deer season) so I'm trying to keep recoil to a minimum.  I have a 30-06 that I use but I think that might be too much for him (don't want him recoil sensitive).  Anyway, the use for deer hunting is very low on the list for this rifle (if at all).

This. But it's cute that you think that single rifle is going to cure BRD (black rifle disease).

It creeps up on you, you'll see another Aero lower for 59.99, then the dreaded PSA email sale flyer, and you'll build about 3 a year. Then it's time for a bigger safe.

In all seriousness, in the AR platform, 300 blackout will work great for deer at reasonable ranges, at least here in the hills. Recoil is not serious, and once he has the platform down, he'll not notice the recoil of the 300. For longer distances, you can get into a PSA 308 for less than 600 now, and recoil on it isn't bad either.

Thanks!  I think I will just build in the .223 (I believe the ammo is cheaper than any other caliber besides .22 and in SHTF scenario ammo would be a lot easier to find from what I've read) and worry about a rifle for him next year.  One thing I failed to mention is that I would prefer the "caged" looked of the handguard (I think at least some of them are called M-Lok?).

You're welcome

Thanks USSRangerSM!  Couple of follow up questions:

1.  Is an 18" barrel best for my application?  I thought I had read 16" is standard but I'm not sure what is best.
2.  It looks like that was is chambered for .223 but someone told me that I should buy 5.56mm.  From what I understood, you can shoot .223 in 5.56 but can't shoot 5.56 in .223.  Is that correct or am I confused.
3.  Should I be concerned with whether the barrel is chrome lined?
4.  Is now a good time to buy or should I wait a month or two for bigger sales (Veterans Day? or Black Friday?  I don't need to buy immediately?

Now is a good time to buy. You gain a little more velocity from the 18, but it's 16 inch will be lighter and will work just as well. 5.56 Chambers is more common and would be the correct one to use. You are correct that you cannot use a 223 in a 556, but can use 556 in 223. Just keep searching Palmetto State daily deal till you find the upper you're looking for for the price you're looking to spend

PSA is an excellent choice, IMO.
I would look at uppers that have Nitride barrels rather than phosphate if your budget allows. Nitride can be found for a similar price but is a much better finish. Nitride does not effect accuracy and protects the entire barrel, unlike chrome lined. Nitride also resists wear similar to chrome lined.  Nitride does not require oil to resist rust, unlike phosphate. IMO, Nitride is the highest quality barrel finish and can be found for a similar price to phosphate on many PSA uppers.

Welcome to ARFCOM, OP.  Couple of threads for you:

https://www.ar15.com/forums/t_1_5/2047298_-270-AR-thread-for-Summer-.html

https://www.ar15.com/forums/t_1_5/2146304_That-Every-Man-Be-Armed-Free-AR-parts-Please-contribute-your-old-parts-.html

This is backwards.
You can shoot .223 in a 5.56 chamber.
It is not recommended to shoot 5.56 in a .223 chamber.

.223, 5.56 and .223 Wylde are the chamber dimensions. .223 and .223 Wylde are different. You can shoot 5.56 or .223 ammo from a .223 Wylde chamber without issues. Using 5.56 in a plain .223 chamber has been argued to be unsafe but your not likely to find a .223 chamber on a new barrel anyway. Stainless barrels are usually the most accurate barrels if you don't mind the silver color or painting them.  
I would personally go with a 16'' barrel for my first AR. That's just me though.

1 - Slightly heavier, will give slightly more velocity, generally precludes mounting a bayonet.

2 - There are 3 basic chambers - .223 Remington (don't shoot 5.56x45mm out of), .223 Wylde (5.56x45mm is fine), and 5.56x45mm (.223 Remington is fine).  The leade before the rifling is longer in the .223 Wylde and 5.56x45mm chambers to cope w/ the slightly higher pressure of mil-spec 5.56x45mm ammo.  The longer leade tends to give accuracy issues, so the Wylde chamber is a compromise between the other two.  .223 Remington chambers are just about only seen on manual bolt actions these days - which is the best action to withstand higher pressure.

3 - No.  Chrome lining was the old method used to extend barrel life, but it tends to reduce accuracy as the chrome lining is not perfectly even.  Ceteris paribus, a non-chrome bbl will be more accurate than a chrome bbl at the beginning of its life, though the accuracy of the non-chrome bbl will degrade faster.  Due to EPA rule changes, chrome plating has gotten much more expensive, so nitriding has come onto the market, which has nearly the same wear resistance as chrome but without the unevenness of chrome plating.  If you can spring for a nitrided bbl, you'll be slightly ahead.  AR barrels are easy to replace, so unlined bbls are a good value and will be accurate for thousands of rounds.

4 - Things are cheap right now, but as we get closer to the mid-terms, expect prices to rise a little.  There's always smoking deals on Black Friday, but it sells out quick and is never in the exact configuration/color you're looking for.

Correct.. I was only on my first cup of coffee

Sorry about that.  I meant the reverse.

What exactly is the gas system?  Palmetto refers to "Carbide", "Mid-Length" and "Rifle".  What does this mean and which would be best for my situation?

Depending on the length of your Barrel, but there is a hole on the top of your Barrel that gases escaped as your bullet is fired and pushes your bolt carrier back in order to eject spent casing and reload new. You only need so much gas to do so, so on a longer Barrel the gas block is further from your bolt carrier then a shorter Barrel

So what would be the appropriate gas system for a 16" barrel?

Carbine length

Carbine length gas is old school.

Go with the new and much improved Mid Length gas system for a 16" barrel.

OP, take a look at this build kit.  Everything you need in one complete package.

https://palmettostatearmory.com/psa-16-mid-length-5-56-nato-1-7-nitride-13-5-lightweight-m-lok-moe-ept-rifle-kit-with-mbus-sight-set-gray-5165449537.html

$350 and Free Shipping.  I was ready to post a link to a $70 toolcraft BCG, but I don't have to.  PSA included their C158 Bolt Carrier Group for you.  Fantastic Deal!

Pros:
CMV4150 + Nitride.
Mid Length Gas
Receiver Extension Tube 7075-T6 (better than 6061)
includes Magpul Back Up Iron Sights (BUIS) so she's ready to shoot once assembled!
Enhanced Polished Trigger is arguably better than a standard mil-spec.

Cons:
Magpul Grip & Stock are Gray - might not be to your liking?
1:7 Twist rate.  You might prefer a 1:8, but it is better than a 1:9.

I agree with a mid-length for the 16 inch barrel...

Cold.

The location of the gas port is a bayonet hilt's length from the muzzle.  On a 14.5" bbl, that's a CARBINE length gas system.  A 16" bbl can use carbine gas, but it will run more smoothly with "MID" gas, or mid-length.  18" bbls use mid-length, or more commonly, rifle gas.  20" bbls (the orginal AR-15 length) use rifle gas.  Barrels longer than 20" generally use rifle gas, although custom length gas tubes can be built.

The length of the gas tube affects the timing of the unlocking action, also referred to as "dwell time".  The closer the gas port is to the muzzle, the longer the bullet will spend in the bbl before passing the gas port, and beginning the unlocking sequence.  The longer the unlocking sequence is delayed, the lower the gas pressure in the case will be, and the easier it will be to extract the case from the chamber.

https://www.aimsurplus.com/product.aspx?item=XAPAR700305M9&name=AERO+Precision+M4E1+.223+Wylde+Barreled+Upper+w%2f+15+in.+ATLAS+S-ONE+Handguard&groupid=4326

Granted, that is a better product.  However Let's compare apples to apples.  You'll have to add:
$90 BCG and CH
$70 Magpul BUIS
$100 Lower Build Kit with stock

So now add $260 to the $400 price.  Do you think it's worth $310 more than the Palmetto State Armory rife kit?

Thanks all.  I ended up with the Palmetto kit (but found it in black for $20 more):

https://palmettostatearmory.com/psa-16-5-56-nato-1-7-mid-length-nitride-13-5-lightweight-m-lok-moe-ctr-ept-rifle-kit-with-mbus-sight-set-5165449492.html

So what tools do I need to assemble now?

You did well.  The kit you purchased has the upgraded Magpul CTR stock.  I’m glad you didn’t pay an extra $20 for just a color change to black.

Check out This post for an idea of tools.

Another thread started asking about tools..

https://www.ar15.com/forums/AR-15/Gathering-the-essential-tools-for-my-first-build-from-scratch-what-am-I-forgetting-/4-731488/