.308 or .30-06 would be good choices.
Unless you're hunting BIG game long-range, all you get from a Magnum is a sore shoulder and an empty wallet.
.308 will get you a short action, which is nice if you want a small, light gun, but otherwise doesn't matter, and it's readily available for cheap. .30-06 allows more flexibility if you want to cook up some handloads, since it has a bigger case, and it's also available for cheap. "Cheap", though, is relative to .300 or 7mm magnums.
For plinking, a .223 is probably a better choice than all of the above. Low recoil, low price, ready availability of match ammo in various bullet weights, as well as surplus and reman practice ammo. Shoots flat enough, and if you don't need the energy of a big bore round, it will hit targets many hundreds of yards away with no trouble.
Run some numbers:
http://www.remington.com/products/ammunition/ballistics/
See this:
http://www.chuckhawks.com/rifle_trajectory_table.htm
You'll see that the .223 doesn't shoot quite as flat as a .30-06, but it's not far off. For long-distance shooting, you'll be doing something to compensate for the drop anyway, whether it's 5" or 8" at 300 yards. Either you'll have a reticle to do it, or you'll turn the scope knob a certain number of clicks.
You CAN shoot 300 yards with a good .22LR, no problem, if you know the bullet drop. Good .22LR means $1000 plus the scope, though. IMO .223 is a decent compromise between the low price of a .22 and the long, flat trajectory of an expensive centerfire.
Just some food for thought.
I have a .30-06, and I'm thinking about getting a .223 boltie for practice.
On the other hand, a .22LR barrel outlasts any of the above, by a LOT.
Low velocity has its advantages.