If you're talking big game in alaska, hands down I would get a .30-06 over a .308, and I would guess many outfitters and others would want you to have something even bigger, though a .30-06 I think for most things there would be the starting point of cartridges.

You really can do it all in N.A. with the '06.

If you were just talking deer hunting....that would be a different discussion. As well if you were talking multiple guns...

From rabbits to brown bear....I'd get a 3 gun combo...1 light, 1 in the middle, and 1 magnum.

.243 Win, a .270 win or .30-06, and probably a .338mag or .375H&H.