Most of the critters I kill are varmints. I don't keep the hides, so I kill them with all my Handis....whatever is in my hand or nearby. If he's out a ways, I'll try to grab something with range. If I can't or don't have time, I grab the closest and fudge the elevation if I have to. If I'm actually hunting fox, coyotes, woodchucks etc. and expect long shots, I'll take the .223, .22-250, .243, 7mm-08 or one of the .308s. As I said, I don't sweat the hole in the critter. The bigger the better. The .243 is the dedicated wolf rifle and should be back at work within a month or so when lambing season arrives. Wolves and coyotes think that's a picnic. The .32-20, the Maxis, .30-30, .38-55 and the .45-70 have taken as many varmints as the "Varmint Rifles".
I believe the choice of bullet is more important than the caliber if you want to keep the hides. I killed a coyote one time with a SKS and a FMJ Ruski round. Poked a pencil hole through him. If a varmint bullet exits, you're going to have a mess on the off side.
Pete