RE: 3 rifles for all North American game
My thoughts are that the 243 is good for small varmint up to deer and the 338 is good for deer on up to the biggest meanest critters up north.
For my own battery I think I would pass on the 243 and move up to a 25 cal for varmints up to deer and a 338 for the rest. But if I went for a 3 gun battery maybe a 223 or 22-250, a mid caliber like a 270 for deer on up to elk and even moose and a big bore like a 338 or larger for the nasties.