The .308 is certainly an excellent cartridge, but I have had great performance out of the .270 as well. Either would do for your uses, including elk, black bear, and moose.

Nikon scopes are acceptable, but I have some issues with Nikon customer (non) service, so I'd buy a Leupold. I have a number of variable-power scopes, but find that whenver game appears, I just use the scope set on whatever powder it happens to be on at the time. So I've started putting 6X fixed-power scopes on all my new, serious hunting rifles. 6X is not too much, even at ranges under 50 yards!