If your'e a reloader, choosing something in the 30-06 or .308 cartridge families would be a good idea since you could neck up or down cases from several different cartridges to fit yours. Pick a cartridge with a bullet diameter that's not SUPER popular, like 25-06 in the '06 family, or .260 in the .308 family.
But an even better idea IMO is to pick a reasonably inexpensive cartridge that fits your bill, and go ahead and be stocked up in advance. If you want something good for any animal in North America, I cant think of anything more versatile than a .30-06
"Most people can't hit a flock of circus tents at those ranges." - P.O. Ackley