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