.223
dont even consider the .222 unless for some reason you want to hunt around for ammo and pay twice as much for it for the same performance. nothing wrong with a .222 if you already own one or someone gives one to you, but to go out and actually buy one seems nuts to me. ballistically it is nearly identical to the .223 but you lose the massive variety of cheap and widely available ammo that is one of the biggest selling points of the .223. if you want to spend more for ammo then get something like the .22-250, that will actually give better performance for the money.
Winchester USA pointed softpoints are dirt cheap and in my experience destroy less of the pelt than the Winchester USA varmint rounds you get in the 40 round bulk packs at Wally World™. the varmint rounds really blow up groundhogs and small varmints though.