Good to know!!!
Let me clarify a few things...
If you want a short barrel rifle (SBR)
regardless of whether you buy it already built or buy the parts to build it, you MUST fill out the paperwork as bkoenig stated, pay your $200 tax stamp, etc.
Regarding building the rest of the rifle, or a non-SBR rifle, you can buy all the parts pre-made. The "lower" is the portion of the gun with the trigger guard, magazine well, pistol grip, etc. THIS is what is considered the firearm by the ATF. The rest of the parts are just...well...parts. You can buy a stripped (no parts, just an empty shell that you add parts to) from MANY manufacturers. So by "building" your own firearm, I was referring to the act of purchasing the pre-made parts and putting them together.
Regarding what "would be best for a SHTF" rifle. There is no perfect rifle and/or caliber. You have to do some reading and make that determination for yourself. Be aware, when you build one, they will start to pro-create and the next thing you know you have six "SHTF rifles". One SBR for close quarters. One 20" barrel for long range. One in .300AAC. One AR-10 (7.62/.308). etc. etc. They are like rabbits or Tribbles.
Check out AR15.com (a.k.a. ARFCOM). Read and be cautious about asking newb questions without doing a COMPLETE search because there are many web commandos that will rip off your head and $hit down your neck for asking a question that they have seen before. Better yet, read on AR15.com, then come back here to get a friendly answer.
I personally am largely inexperienced in the AR-15, or most rifles for that matter, but there are many hear with great amounts of knowledge on the subject.
Fly