Truth be told, in most loads, the .223 rem is only about 100-200fps behind the .22-250, and when you're pushing 4000fps, a hundred here and there don't make much difference.

The big difference in the two is that the .22-250 typically handles heavier bullets better because of tighter twist rates, so they fight the wind better out there at longer ranges.

One thing I'll suggest, what you're talking about is a target rifle, so "cheap ammo" availability shouldn't really be a consideration, since it's rare that target grade stuff is really much cheaper from one cartridge to another. There's no sense in putting crappy surplus crap in your nice target rifle.

I'm a .22-250 fan myself, as far as bolt guns go...I'd really rather take my AR-15 out as opposed to my bolt guns, but for LONG ranges the bolt guns win out (not by much), I occasionally take my .308win out for serious long range shooting.

You'll likely NEVER notice the difference, and neither will your game!!