22-250 I have both and even though I have extensive experience with the .223 at distances considered extreme to this posting (out to 500 yds without optical sight), I still prefer the 22-250. If you purchase the heavy barreled version of whatever rifle brand you choose (I suggest it) there will not be a substancial gain in recoil over the .223.

Surplus military ammo for the .223 usually will not be corrosive and will not "burn out" your barrel any faster than factory ammo. As for price if you are using quality ammo you will not see a great difference in price. If you are looking for accuracy I'm sure you will not be shooting cheap military surplus or the cheap Russian made ammo anyway. The bullet design of the military ammo will not perform on small game as you might expect. A FMJ round will not expand greatly from a 223, much less with a steel core vrs. a lead core.