Disclaimer 1 - Already have an AR15If you already own an AR15 now, that is not of a configuration as listed below, do not panic! Any AR15 is better than no AR15. The primary objective is to get competent with what you have. After that, you will want to build the rifle around what you want to do with it and what you need to be able to do with it.A perfectly acceptable option would be to get competent, then upgrade the rifle as funds permit. The neat thing about the AR15 is that it is highly customizable.
Disclaimer 2 - Alternate Rifles
As surely as I will put this up, there will be an M14 fan or some-such that will come on here and try to tell me that their rifle is better than an AR15 for this reason or that.
However, there is no doubt that when the factors of reliability, ammo commonality, parts availability, effectiveness, range, speed, weight, expense, maintenance, shot capacity, etc.; the AR15 clearly is the most well-rounded rifle on the market.
The Original Is Your Best Bet
When Stoner created the AR15 rifle, he did his homework. The original M16 had a 20" barrel, rifle length gas system, and rifle buffer tube. Since then, many alternative barrels, gas systems, and buffer tubes have been created, but none are quite as effective as the above combination.
The 20" barrel offers the best projectile velocity, at a manageable weight for the user. Some may select a government profile barrel - most of which should be accurate to within 2 minutes of angle (MOA). That means if you do your part, the rifle can put all rounds within a 12" circle at 600 yards. That is more than good enough for a rifleman.
An 18" barrel would be a second choice. Get one only with a rifle length gas system.
A 16" (or 14.5") barrel would be less than ideal because of all the lost bullet velocity.
Rifle length gas system
The rifle length gas system is what the system was designed around. It produces the least stress on the bolt and the least recoil to the shooter. It is also the most reliable of the gas systems.
The midlength gas system is better than the carbine gas system, but not as good as the rifle.
Broken bolts and extractors are commonly associated with the carbine length gas system. Ever hear of a 20" rifle shooter looking for a different buffer, etc.? Nope. There's a reason. The carbine length gas system puts the most stress on the bolt, and the most recoil for the shooter.
OK, here is where I will yield quickly. The A2 stock is long, and therefore, somewhat uncomfortable for most shooters. With a rifle length gas system in place, the buffer tube becomes far less important to overall reliability. If you want an A1 stock, or a collapsible stock, go ahead and get one... and don't look back.
Most barrels these days are 1:7 (one twist every 7 inches) or 1:9. Either is fine. Do not worry about it. If you have a specific need to shoot bullets heavier than 75 grain, then you need to build another rifle for that specific purpose. 1:8 is also good.
The only barrel I'd avoid is the pencil-barrel. Its accuracy will degrade more as the barrel heats up. A heavy barrel is fine, a .gov profile barrel is fine. Free-float is fine. Non free-float is fine.
Chrome-lined is fine.
Chrome-moly is fine.
Stainless steel is fine.
You should practice, practice, practice. That said, the cheapest brass-cased ammo comes in one of two major types: 55-grain (M193 clone) or 62-grain (M855 clone). In most rifles, an M193 clone ammo will shoot to the same point of impact (POI) as an M855 clone. Pick one of these (or both) to stock up on it.
Generally speaking, 55-grain stuff is more accurate. (often around 2 MOA)
Generally speaking, 62-grain stuff bucks wind better at a distance. (often around 4 MOA accuracy)
Most self defense takes place inside of 21 feet, and there will be very few times in a potential SHTF scenario that you will need to shoot past 100 yards.
Training done under 100 yards can be done with steel cased ammo. Do not bulk up on steel cased ammo for self defense or SHTF.
Magazines are a must. Generally, you will want to have 30-round magazines if state law permits. If you have one magazine, you are on your way. Next comes two magazines. Next goal is ten. I prefer Magpul's PMAGs due to reliability. However, USGI style mags can be good... make sure to test them before relying on them.
Here is a list of types of sights from least to most desirable:
Fixed-plane iron sight - least desirable (good as a backup iron sight).
Adjustable for bullet drop iron sight (carry handle, KAC, "chopped carry handle," etc.)
Small scope - Burris 332 / Primary Arms PAC3X
What I've described above in an M16A4 clone or substantially similar. Whether you get rails or not is up to you. If you want a quad rail, and to free float the barrel, a LaRue quad rail is really hard to beat.