I just bought an AR and a nice target varmint rife. In my mind, I want both, they are really for doing different things though. The AR is for fun, plinking and targets out to 100 yards. A fun gun for my kids to shoot or if I want to take a friend who hasn't shot before. Also a good defensive weapon for the aftermath of the 9.0 earthquake we will have someday. The varmint is for targets and punching paper at 200-300 yards. Both are .223/5.56 so I can share ammo.
I briefly considered getting the varmint rifle in .308 or .30-06 but the difference in ammo prices meant that I would not be able to afford to put many rounds between either large caliber. I bought 1,000 rounds of PMC Bronze 55 grain .223 for $275.00 today. That is factory fresh new ammo, not reloads. That is affordable to me.
Between the two disciplines, fun gun or target/varmint, target shooting at a distance seems like it will be a lot more interesting. Plinking and fast fire with an AR is fun but that can get old quicker. So my vote is for the target gun first.