Info needed on a Varmint rig set up

[scott_r]

You need a 204 ruger less pelt damage than the 22-250 and better trajectory than 223.

I've shot a tonne of coyotes and have never had much pelt damage from a 22-250. Use a frangible bullet like a 55 gr V-Max and it will not exit on a chest shot. I've also used 55 gr. Sierra HP's w/ great success.
I would not rule out a .243 if you're looking to shoot at longer ranges.