I'm about to order an LMT upper but I want to pick the right bolt and carrier combo.

I can get the:

LMT Chrome bolt and carrier with the upper for $110 (This is not the LMT Modified bolt)
Colt Ar-15 Bolt and carrier
Colt M-16 Bolt and carrier
Others?

I just need some imput, this will be the first rifle I build so I want to do it right.

Thanks

Also correct me if i'm wrong, but a new upper with a new bolt should not need to be headspaced. Correct?

"The Right One" depends on what you want. For your first build I'd get the LMT. They make excellent parts and their bolt & carrier will fit their upper.

As for headspacing, ALL RIFLES AND BOLTS SHOULD HAVE THE HEADSPACING CHECKED!

Doesn't matter if it is Colt, LMT, Bushmaster, or whatever.

I would stay away from "chrome bolts", they have the nasty reputation of breaking in half.  I know there will be those who say they have never had a problem, but when there are those who have had them break (and this is a VERY dangerous condition) why would anyone take the chance.  I have never seen a black bolt break, never.  Hydrogen embrittlement is the culprit here, when chrome plating is done it causes the surface of the underlying metal to become brittle.  Federal law prohibits many aircraft parts and the front rims of commercial vehicles from being chrome plated due to this exact reason, so don't go for it.  I have never seen any problems with chrome plated carriers as this part does not take the forces that the bolt does, chrome it easier to clean, looks good and costs more.  If you must have chrome, see if whoever you buy from will give you a mp (manganese phosphate) black bolt on a chrome carrier.  You will still have ease of cleaning and good looks to, but you will be safe from the gun exploding in your face!  After buying two chrome bolt/carriers combos, I've scrapped the bolts for headspace checking only and now only use black on black, there is nothing wrong with them except maybe requiring more lube after many hundreds of rounds fired.

Braking chromed bolts has to do with a poor chrome job and embrittlement.  If you stick with a quality mfg of chrome bolts like KAC, LBC/Young, or LMT I don't think that will happen and I endorse those all wholeheartedly.  The LMT I think may be nickeled and not chrome, at least that's what they look like to me. Assuming your LMT upper is longer than 11.5", I recommend the LBC Chrome Carrier and LMT Bolt as one of the ultimate combos.  I am recently liking the SE stainless steel carrier, but the LBC has some other design features going for it like having the weight equal to a standard M16 carrier among other things.  I have an LMT Carrier (standard) but I got it labeled as a KAC Match carrier but I found out it's a chromed LMT.  My second choice in bolts would be the Colt bolt due to the supposed micropolishing and finish work on the bolt face and extractor, besides flat out quality and test tolerance.  You can't go wrong with a Colt Carrier and bolt, but I there are superior carriers and bolts IMHO but the differences may not be worth it to you and your budget.

In all likelyhood you should not have to headspace as long as the bolt and upper/barrel is from a good manufacturer.  It's more of a peace of mind issue as a bad headspace is extremely rare.  To me it's like getting a car.  There's always a chance the manufacturer did something wrong and it could blow up or have a possible fatal malfunction, but the chances are minimal.  No one I know checks every little part on their car when they get it, they trust in the manufacture.  Of course people still die every year from defective cars so by all means, nothing wrong with checking headspace.  I've done lots of bolts and uppers and none have even come close to being out of headspace but I blew the money for the gauges so what the heck.  I'll always feel it was a waste of money unless one day I come across one that doesn't headspace (probably be a blue moon out that night).