Two options, in this hunting forum: You're hunting in either big-bear country or in little-bear country.
Big bear country, you have some sort of rifle that could deal with Mr. Brownie, I guess, as well as do in a moose or caribou. That's generally somewhere around a .300 WinMag or more. Handgun? You might want to think for survival that hares or ptarmigan or suchlike could be on the menu, so the usual .22 critter.
Little bear country? Whatever's suitable for the hunting you'd planned on. If Bambi, odds are that anything from a .30-30 on up would work just fine. Same as before for a handgun, although if you are concerned about a higher probability of Bad People, any self-defense handgun should do.
But if you're a really good hunter, odds are that you'll spot Bad Guys before they know you're around. The average Bad Guy is likely not a good hunter; the average hunter is likely not a Bad Guy. That's part of Condition Yellow--knowing your environment and what's in it and what you might do to deal with problems.
Note: A bunch of nonsense about survival in any SHTF deal means this thread won't survive.