.62cal/.20ga or .54cal/.28ga both get it done easily for the game you mentioned at the distances those small game are normally taken.
Now if you start getting into all sorts of thinking like one day you might win the lottery and take a once in a lifetime moose hunting trip to Maine, then the .62cal would give you that flexibility.
You just have to be realistic with yourself in terms of what you're really going to use it for, year in and year out, and make the decision.
But for the game you listed in your original post, I'd never regret having a good .54cal/.28ga to hunt them...and they also shoot PRBs like a house-afire if you want to go deer hunting.