Got an opportunity to do some varmint hunting where there is a sizable population of grey fox. Looking to find a good one for a full body mount. Ant suggestions on the best caliber for the least pelt damage and best shot placement.

If there are no coyotes and your just shooting fox 22mag/17HMR/17Hornet would be the best bet to save pelt damage but all are lacking if coyotes are in the picture.
Then it's 22Hornet /221Fireball /222Rem/223 with proper ammo and your Ok for both. If you handload shouldn't be too hard to work up a load that kills well with minimal damage. In .224 caliber factory stuff it gets a little dicey on ammo that performs well without blowing holes in fox.

.22

Thanks. Very few coyotes, primary target will be fox. Thanks for the advice

.17 hmr will hammer them out to 100 yards or more

Shotgun with number 4 shot

12 ga will be your best bet.

Back in the day when fur was bringing money and I was shooting for the best pelts possible I dropped a lot of cats and foxes with a .17 Rem. or a .218 Bee.

.17 Rem.

22 Magnum, 17 HMR, 22LR are all good choices for fox. If you are planning on possible shots over 75 yards I'd think about a 223 with a bonded bullet like a partition, pro hunter, etc to avoid any expansion and small exit hole.