For the use you described, I would go with .223R/5.56mil. in either a Savage or a Remington HB. Either would be accurate enough with mil. surplus ammo and both could be tack drivers with top quality commercial ammo or good handloads. The .243 Win. cartridge would be a good prairie dog rifle out a few yards further than the .223R but becomes very expensive unless you handload. So, I guess your decision depends on just how much you intend to shoot. When I was serious about PD hunting I took 5 ea. dedicated rifle/cartridge combos to cover all distances out to 1000 yds. They were; .223R, 22-250, .243 Ackley Improved, 250 Sav. Ackley Improved and 6.5x06. All were heavy barreled Remington 700s. I was also known to take a 22 Hornet Ackley Improved when the PDs were especially abundant and close to my shooting positions. Obviously that sort of PD hunting involved a lot of handloading.
For you to sort of ease into this longer range precision shooting, IMHO, start with a non wildcat and something you can buy ammo at a reasonable price. Therefore my recommendation on the .223R caliber with a Wylde chamber to be able to shoot all the military ammo you wish. And, the rifle wouldn't have to be a bolt gun since there are many very heavy barrel AR-15 types available now that will shoot under 1/2 m.o.a. .............