I'm no magnum hater, but if you're inexperienced with rifles and start off with a lightweight .300 WM, you may become one in very short order. If not a rifle hater altogether. At best I can virtually guarantee you will begin your rifle-shooting career by developing a flinch that will be hard to break.
Did your first bow have a 75-lb draw?
A .300 magnum is not going to give you any significant advantage hunting elk. Period.
+1 on the .30-06 or .280 Remington. If elk/moose are a likelihood, I would lean towards the .30-06. Once you've put a couple thousand rounds through it, if you still want a magnum, you'll then be ready for it.
I'm sure this will be met with all manner of indignant replies stating "I've shot a 100 deer at 500 yards, blah blah". But the truth is, there are very few hunters who have any business shooting at a deer, under true field conditions, at a range where the trajectory of the faster bullet would make a difference (and I'd call that 250+ yards.)
And by true field conditions, I mean not snug in a stand that's the equivalent of shooting off the bench with a heavy-barrel rifle.