I've got a match grade .22, a .22 Hornet, a CZ American in Ruger .204, an ultra accurate AR 223, and a Remington 700 VS heavy barrel in 22-250.
As noted, it depends a lot on how much you're gonna shoot, do you hand load (I assume not if you have to ask which to buy), and as noted, the anticipated ranges.
If I had to pick one to take on a prairie dog hunt (lots of shots and accuracy required), it would be the AR closely followed by the .204. In a few weeks the lunacy will die down and .223 ammo will most likely be cheap again. The .204 shoots laser flat and has zero recoil.
Third would be the Hornet, and the .22-250 would be last, simply because the barrel heats really fast (as in five shots or less), it has a little more recoil (can't see the hits), and it's LOUD.
Back nearly fifty years ago my dad bought me a 22-250. I terrorized groundhogs around the farming community. There are other choices I'd make now.
Any/all would be acceptable. Anything above these start to punish you in the recoil and noise departments.