For deer it is excellent. Moose or Elk IMO is a little light, but if you limited yourself on range and shots it might make do. If you are worried about recoil what about a 308 or 3006? They will allow you to bullet grade up or down and kick a little more than the 7mm-08 but definitely tolerable. When I started hunting at 12 I used a 308, my buddy a 3006 I can't think that either one of us complained about the kick.

Maybe if possible try shooting a few different calibers and see what will suit your needs and recoil. You maybe suprised how much you can comfortably handle!!!