I should start by asking a question nobody else has asked yet...when you say, "in the United States", does that mean you aren't originally from the U.S.? The only reason I ask is because you have to be a Permanent Resident to buy a firearm. But maybe you knew that already, so I apologize if I'm telling you anything that is irrelevant.
In my opinion, an AR-15 in .223 is a perfectly sane choice for a first long gun if you have $2,000 to spend. AKs are fun, too, but they're usually purchased by people who (A.) can't afford ARs, or (B.) just want to have one for collection purposes (i.e. myself). ARs are fairly easy for most people new to long guns to master; most people find it easy to shoot good shot groups at 25 yards almost as soon as they pick up the weapon (well, OK, after zeroing, of course
). I own both an AR and an AK, and the AR is all I ever shoot these days.
As far as a .22 goes: Screw it. .22s are for kids who haven't hit puberty yet (or really, really skinny girls). For someone your age and size, you won't have any more problems with a .223 than you'd have with a .22. Plus, .22s just feel like toys. The ammo cost is the only advantage, and I'm of the opinion that you might as well just save for something in a larger caliber and get the most fun out of the experience. Even for plinking, an AR-15 is a good choice. You can get one of the cheaper models that's made for people who only intend to plink; I recommend checking out the "Plinker Plus" line from Olympic Arms for a start.
Oh, and unless you plan to do serious target shooting, forget about anything chambered in .308. I don't know anybody who owns a .308 and enjoys shooting it just for fun. The guys who own M1As and Remy 700s are the types of dudes who will buy the rifle and then put down another $2-$3 Grande replacing the barrel, scope, stock, and almost everything that the rifle comes with from the factory. My uncle owns an M1A that he almost never shoots (he once told me that he only bought it out of nostalgia - the M14 was what he trained on in ROTC).