I use a .220 Swift ( Rugar ).. it seems to do the job.

i hunt for fur and if your wanting to then your bet choices will be:
17 rem, 223 rem, 204 ruger, 218 bee, 221 fireball, 22 hornet, are my choices. my 223 is a 223 ackley though. the 220 swift wont do very well though. the 243 is way to hard on em if your fur hunting and the 22-250 is def not a choice for me unless u shoot a very very light bullet. but thats just me.

I built a custom coyote gun on a Remington 700 action. Lots of money in this gun but it's shoots great.. I did choose 22-250 and love it. I'm not so much after pelts though, the bigger the hole the better.. lol
One I hit this year left a hole on opposite shoulder about the size of a softball..

But if you wants pelts I'd build a 223.

Good Luck

i suppose if your a hand loader you can always load them down if your hunting fur