Ha, great title.
The rifle would be used for target shooting and maybe some deer or hog hunting, maybe even caribou if I get the urge. I also sort of like the idea of longer range competition shooting but have never done any.
Just my opinion, but I think that to cover all these intended uses, an AR (if you really want an AR) in .308 would suit your needs far better than one in .223. .223 is debateable in deer. I happen to think that with the proper bullets and good shot placement, it is enough. Others disagree to the point of calling it unethical. Kind of the same deal with hogs, although again, I think it is enough. Caribou... Probably can be done, but certainly .223 isn't anywhere near the best choice. Long range shooting can be done with a .223, provided that your long range doesn't mean much past 600 yards or so.
Don't get me wrong, I love the .223. I have 4 rifles chambered so, and only 2 of them are AR's. I just think that for your intended uses, you would be much, much happier with the .308 version. Even in cases where the .223 would be enough, the .308 would be better, and it extends your range for accurate target shooting substantially. The .308 is easy to reload, big enough for most anything you would shoot on this continent, and there are plenty of commercial loads if your not into reloading. I would also add that it is very, very popular and will thus be easy to find ammo for, even at Walmart.
Take it for what it's worth from a fan of both AR's and the .223: Get a .308.
Edit to add: Texas Rifleman is correct, by the way. An AR in .308 can be had for well under $1500.00. $1200.00 is pretty much spot on, but you might luck out and find one for even less. I don't have any problems with any of the other rifles mentioned, but none of them will beat an AR for accuracy on average. You might be able to find one particular FAL or Saiga or whatever that will best one particular AR, but on average the AR is always going to win that contest. That being said, the Saiga is a pretty good value. I own one in 7.62x39 with the modification done so that it will accept AK mags and my Dad owns one in .308, and both are nice shooters.