Re: 22-250 rem
for coyotes--you need a good hit, so my personal limit would be 600 for them. For prairie dogs and chucks i would shoot as far as i could see the bullet impact.
It would probably take a centered shot at 1k to kill a PD, but you never now--they are not put together real well--a groundhog though is much tougher.
I like to stretch the legs of any cartridge i use, especially when it comes to varmints, you will have to come up with your own personal limits. I will tell you this, i see my 223 with 50gn vmax as a no problem 500 yard gun for varmints, so with 300fps more...
you will have to make your own decision based on your ability, the rifle, and the load you come up with.