If it's like coyote size and smaller, 22-250 without a shadow of a doubt. A 35gr Nosler BT at 4,435fps is a wonder to behold. It's almost unfair.
If I'm including deer, 260 for sure. Partly because I like to be different, partly because it picks up pretty much where the 243 leaves off, which is at the low end for big game and still low enough for varmints.
I don't care much for 243. Don't know why. I guess it just seems like an intermediate, niche cartridge that's realistically too big for my woodchuck hunting and smaller than I would pick for deer. It's entirely adequate for deer, absolutely without a doubt, but it's not the best choice IMO.
260 is perfect for deer, acceptable for woodchucks and coyote. 22-250 is absolutely awesome for anything up to coyote size.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.