If you just want one rifle, the 30-06 is hard to beat. Accurate, abundant power, good trajectory, most popular hunting round by far, ammunition available everywhere, more avaible loads than any other round, fairly cheap to shoot, moderate recoil, excellent for everything from pronghorn to grizzly, etc.
My second choice would be one of the 300 mags. They increase your range by 30-60 yards, but there are substantial trade-offs as far as recoil, ammo expense, and magazine capacity.
The 270, 7mag and the like are good calibers, but I think they are a little small for big bull elk or big bears. You might be wise to get a really big gun (338, 375) for the rare occassion when you get to hunt such game.