I'll disagree a bit with some of the earlier wisdom. If I'm hunting a predator who could quickly turn the tables, I'm not interested in a 'fair fight'. I'm interested in a shot that's close being a kill shot. That usually translates to a larger caliber / cartridge, or more rapid fire capability.
.300 Win Mag or the .308 is about the minimum I'd want to go with out of your list.
أنا لست ارهابيا
.50 BMG: 1 Shot 1 THRILL!