I'd stay away from lever action rifles for hunting.  lever action rifles use tubular magazines.  tubular magazines limit you to round-nose bullets.  round-nose rounds are not as stable in flight, bleed off energy faster, and the end result is a lot faster drop.
I'd go with a bolt action, and if you are loading your own rounds, a boat-tailed spire-point for projectiles.
.30-06 is a great all purpose round, hits hard enough for elk, not over-kill on deer.
.300 mag if you want a little more punch.