Although a .308 will work, I'd rather shoot a moose with the .30-06 - all else equal, it's a better choice because of the added velocity.
Stick with 180 grain premium bullets, like Nosler Partitions, Barnes X, Swift-A-Frames, Trophy Bonded, etc.
If recoil is not a problem, then you can look at Federal's High Energy loads, which boost velocity by about 200 fps.
Zachary