Though I don't ascribe much to the one gun for all theory, if I had to limit myself to one rifle only it would be in 30/06.
Preferably a Mauser 98 action, Winchester 3 position safety, upgraded trigger, (Timney or such) 4X fixed power scope, synthetic stock, detachable sling, pillar bedded and free floated. It wouldn't make me ooh or aah with finely figured walnut or flashy high-gloss blue, or telescopic sights to shoot 1000 yards, but it would put a lot of meat in the pot from little things to big things.
Probably use 180 grain bullets all the time for deer to larger elk and moose, but would just change the style of bullet construction to match the game. For littler stuff I'd try to find some 125 gr or 130 gr bullets that would behave.