Well, if ranges aren't too extreme, I think a .35 Whelen(not too bad, I've been shooting 250 grainers since I've been 15)would be a good choice. Or you could go with my personal favorite calibre, the 6.5x55 Swede (extremely low recoil, but hard hitting)
I've heard people taking moose withthe 6.5(Rebel Hog, I'm talking about you), so I'll assume it'll take a elk. Both aren't extremely long range calibres (I'd said under 200 yards, especially if you go with the 6.5 for elk, and limit yourself to broadside), but other than that, I'd say you're good to go.
Cory