If you really want to hunt with a lever-action, look into the Browning Lever Rifle, or BLR, it's chambered in .308, as well as lots of other calibers.
Of course, if you go with any lever-action, accuracy will suffer.

I would say go with the Howa bolt-action, better hunting rifle, would work great for deer,elk, moose, bear, antelope, and other game animals.

DMPS would be a fun rifle, for shooting, but AR-10's aren't known to be ideal hunting rifles for big game.