i used a 22-250 thoughout my younger years to get beer money from coyotes hides, now shoot a 223, have bolt gun and AR platform, still have the 22-250 but my calling has gotten better over the last 30yrs, carry a shot gun with me. 243 little heavy unless you are in windy area, when i go to wyoming to hunt them i do take a 243 with me
if i had only 1: it would be 223 - good stopping power, find ammo anyplace, no recoil, fun to shoot
put a good scope on it. Dont overpower with the scope, 3-9 is as big as you need
If they are in a trap and you just need to dispatch them then the .22 mag will work fine. It will also be a good round for foxes, but when you go up to the size of a coyote you need a little bit more fire power so the .223 gets the nod. That is unless you don't plan on using the hides or want a longer range shot and then I like the .22-250 and as long as you use the right ammo or use head shots then pelt damage should be kept to a minimum.
First off welcome to BGH, always glad to see new folks on here. If you're planning on a new gun I would go with a 22-250 for sure. Not as much damage to the hide especially on a smaller fox, bobcat, badger etc. Hope to see some photos and read some stories of your hunts.
When hunting whitetails there are many different languages being spoken afield that I key on when outdoors. All these little creatures living around whitetails have something to tell us if we are willing to listen.
My favorite tattletales of the outdoors are a handful of little birds that live in my state of Ohio. Maybe yours too. A tip for the upcoming season.
There are Blue Jays, Cardinals, Chickadees, Killdeer, and Sparrows that all have language...