When you say you don't understand the rifle and acronyms it wouldn't hurt to read these articles on the AR-15/M16/M4 and don't be afraid to click the hot links for more info.
AR-15 - Wikipedia, the free encyclopedia
M16 rifle - Wikipedia, the free encyclopedia
Google will likely give you a decent answer too, though you may have to sort through hits that apply.
Carbine length gas system refers to a 7" gas system, midlength is 2" longer and rifle length is about 2" more. Not directly related to barrel length.
The biggest issue with assembling an AR isn't so much getting the parts together right - it's getting the right parts together.
US Army 1966-69, VFW Life Member, Retired Geek