Quick-and-dirty rundown
Upper receiver types:
A1 - "Original" style upper receiver. Does not have a forward assist. Integral rear sight and carry handle. You won't see many of these.
A2 - Basically same as above, but has forward assist.
A3 - "Flat top" receiver. No rear sight and carry handle. Has Weaver base.
M4 - Also "flat top," and has some notches in the feed ramp to improve feeding under some conditions.
Barrel lengths/fore ends.
Standard = 20" barrel with 12" fore end.
Carbine = 16" barrel with 7" fore end.
Mid-length = 16" barrel with 9" fore end.
M4 = 14.5" barrel with 7" fore end.
Standard fore ends attach to the barrel nut and at the gas block. "Free floating" fore ends only attach at the barrel nut and do not touch the barrel at the gas block. These are useful for mounting accessories without putting stress on the barrel.
Common abbreviations:
HBAR = Heavy barrel.
LBAR = Lightweight (thinner) barrel.
CAR = Carbine. Rifle equipped with 16" barrel and an adjustable stock.
"M4gery" = M4+"Forgery" - M4 upper, 16" "civilian legal" barrel with a cutout in the barrel for mounting of the M203 grenade launcher (original M4's are 14.5", which is an NFA weapon). Also has an adjustable stock.
SBR = Short Barreled Rifle. Barrel shorter than 16". This is an NFA weapon: tax and registration applies.
You need:
1. Stripped lower receiver. This is the only part you have to get transferred through an FFL.
2. Completed upper receiver. Includes upper receiver casting and installed barrel, gas block, handguard, etc.
3. Bolt, bolt carrier, and charging handle. These are sold with SOME complete uppers. Make sure your upper comes with this, as a bolt and bolt carrier will cost about $100 if you buy them separately from the upper.
4. If you get a flat-top receiver, you will need a scope or rear sight of some kind.
5. Lower parts kit. This includes the fire control system, bolt catch, magazine catch, grip, takedown pins and some roll pins and springs.
6. Buffer tube assembly (including buffer and spring) and stock, whether it be fixed or adjustable.
7. Tools. At the very least you will need a 1/8 pin punch, a hammer, a pair of long nose pliers and a flat head screwdriver. Additionally, you really need a set of roll pin punches if you want to put in the pins without marring the finish on your lower receiver. They are not expensive.
8. If you choose an adjustable stock, you will need a buffer tube nut wrench (~$4).
9. At least one magazine.
Many suppliers sell a "Rifle kit" which includes everything you need except the stripped lower, magazine and tools. This will give you the best price--they put a pretty heavy discount on the kit. It took me about 2 hours to put mine together, and that included a trip to the store to get some roll pin punches. Tip: Work inside a plastic bag when installing the takedown pins. It keeps tiny springs and detents from flying across the room.
Suppliers:
There are many, this is a very short list. Look around for many more.
Del-Ton
www.del-ton.com
M & A Parts
www.m-aparts.com
Bravo Company USA
www.bravocompanyusa.com
J & T Distributing
www.jtdistributing.com
Coleman Tyler
www.colemantyler.com
I chose Del-Ton for mine, mainly due to price. I was very pleased.
Assembly help and more info here:
http://www.ar15.com/content/guides/assembly/lower/
http://ar15.com/forums/topic.html?b=3&f=4&t=226782
Happy building!