It looks like you're narrowing things down to groundhogs, beavers and coons and they will all likely be at shorter range (70 yards or closer). Since preventing pelt damage on those smaller animals seems to be your primary issue, you're not reloading and ammo costs are not a factor, it looks like 22 Mag would do just fine. If those pelts are profitable enough, you could earn enough to pick up a 22 Hornet later and be covered for everything.

There are other guys on this board who have extensive experience with all of the animals you're mentioned and could fine tune your selection even better, especially with ammo selection. My experience is more with coyotes on up and at longer distances out here in the West. I rarely see foxes and bobcats and they require something smaller in caliber than a yote. Not to throw a wrench into your caliber selection plans but my next purchases will likely be a 17 Hornet and 17 WSM for shooting bobcats and foxes with enough steam left for coyotes when needed.