A new hunter - new shooter as well? Perhaps low experience shooting?

One of the old standards, .308 Winchester, .30/06 Winchester, hate to say it, .270 Winchester, 7mm08 Winchester or .260 Remington will do what you want.

I would definitely suggest that you stay away from any belted magnum, ie: no 7mm rem Mag, or short magnum due to the very much increased noise and increased recoil.

Within a new hunter's accuracy range and beyond, all of the above will work perfectly on deer, bear, elk and moose.

The requisite accuracy cannot be replaced with more power and a poor shot with a magnum is a poor shot, it's as sinple as that - the 'extra power' will not get you out of trouble, but can most easily cause it due to innacuracy from flinching.

Every guide out there is witness to this - new hunters with guns too big for their experience levels results in wounded and sometimes lost game.

[edited to include] - bolt action only!