My favorite is the 22-250, but I don' t hunt for pelts so I don' t worry about damage to the hides. The .223 is also an excellent round that would be a little easier on hides. Of course a lot depends upon bullet selection.

There are a number of rounds that will work, 222, 223, 22-250, 220 swift, .243, .308, etc., and of course many of the new short rounds. You sure don' t need a magnum of any kind. In a varmint gun I look for an accurate rifle that won' t beat me to death recoil wise. Some folks are big on the AR-15 type rifles, but I prefer a nice bolt action. I normally select heavy barrels for accuracy and steady hold, but an accurate sporter weight rifle will be easier to carry and manuver.