The 308 will work on anything you mentioned, with the proper bullet and shot placement. There is not much difference in a 308 and a 30-06, not enough to make a difference, a animal definitely cannot tell the difference in the two. As far as going bigger, the only gun bigger that I would own, and do own is a 338 Win mag., but it isn't needed if you have a 308. I have one but hardly ever use it. I shoot a 280 Rem and have killed every thing from coyotes to Buffalo with it.