The .220 Swift is the best choice out of the larger Calibers You mentioned.
Once You get into Coyote/Predator Hunting and decide You want to have a Coyote,Fox or Bobcat mounted You'll find a lighter caliber Gun is the route to take in doing less hide/fur damage or if You give the Predators away to a Trapper that will take the time to skin them out and sell the hides then less damage is what You should strive for.
A lighter weight bullet will go faster and shoot flatter at longer distances and a bullet like a V-max or ballistic tip bullet should be easier on the hides!