If I only had 3 centerfire rifles for everything in North America, they would be a 5.56 AR-15, a 6mm Creedmoor bolt rifle, and a 338 Win Mag, with a close second place in that role for 416 Ruger. The AR for coyotes and small game, 6 creed for longer range coyotes and deer, then the 338 for anything larger than 300lbs.

If you want to tame recoil in the more powerful rifles, add weight. Really that easy.