I'd get a 300 Winchester Magnum. Elk is the biggest game you mention you might hunt. The 300 WM is flat shooting and capable of making the long shots sometimes needed in elk country. A .338 WM is more powerful but with the heavier bullets, it will knock you around quite a bit more. If you are like me, you'll shoot the 300 better. Use a quality 180 gr. bullet in the 300 and you won't go wrong. You may get a chance to hunt Canadian caribou and the 300 would be an excellent choice for them. The lever action suggestions are interesting - my father in law hunted elk for years with a 45-70 Winchester 86 and never needed more than one shot to put them down, but that was timber hunting at short range. If you pay big bucks for an elk hunt, you'll probably want a rifle capable of making long shots as they may be required to bring home a bull.
