If we exclude Western hunting, which can require putting down animals at long distance with authority in nasty places, I'd say any standard action .30cal (except the .30-30, which limits effective range for most shooters even in the East). You don't have to think about shooting special bullets. It just works.
As my username has long heralded, the .308 Win. works great—I like a .60 cal exit wound, and a shot through the vitals with a plain (non-bonded) soft point bullet gives me just that. I also like the .30-06. It's great to be able to punch a shoulder quartering-toward with no hesitation, if needed.
But my dad has done good with 6.5-6.8mm cartridges (including the man bun). His bullet selection has to be a bit more deliberate, though.
If, by the grace of God, I get to do a DIY Western elk trip one day, I'd love to pick up a .300 Win Mag for the extra distance capability thanks to higher velocity.