Bullwhip. It would depend on how much shooting experience you have withbhigh powered rifles. Pete80's advice is good for a seasoned shooter, but if you are just getting into the game, might be just a bit much.
If where you plan to hunt moose or elk also has big bears (Brer Griz) then I would suggest nothing smaller than a 30-06. There are certain advantages to the 06 that you may not find in other calibers. The availability of ammo is one of the most important ones. Various bullet weights for different types of game. (150 gr. bullets for deer, 180's for elk and moose, and even 220 gr. for big bears.) The only drawback to that, it you will probably (most likely) have to resight your rifle when you change bullet weights.
The big problem with any .300 Magnum, is they kick much harder than the 06.
I am basing my opinion on the basis that you are a newbie to the shooting and hunting scene. If you are reasonably well experienced in hunting and shooting, then by all means, use a .300 Magnum.
Paul B.