Any will do.
The most dangerous creature you will ever meet in the woods is man. That's not to say the woods are totally safe, but it's a lot safer than any city.
I've seen other forums where idiots recommend monster guns - 460 calibers and up - as if dinosaurs still roamed the earth. City folks make me laugh. I've roamed West Virginia woods since I was about 12 or so, and never carried anything larger than a sizable Bowie knife
Chances are you'll NEVER be in danger from animals. You might have to worry about pot growers (most of them are just stupid hippies) or, maybe, dumb rednecks, (although they tend to avoid the woods).
The only truly dangerous animals will be a black bear, (attacks are very, very rare) or California cougars (And frankly, who cares - they just eat runners & yuppie liberals).
What I worry about is escaped/semi-domesticated male deer (bucks) filled with testosterone (deer farms are becoming more popular). This is the "domesticated" wild animal responsible for more human fatalities than all other "domesticated" wild animals combined. These critters will attack you in the suburbs.
Bucks and rabid animals (again, very unlikely) are about the only worry you have.
You'll also hear about danger from wolves, but that's crap. Wild dogs are more dangerous, but that's also mostly crap. And you can kill a snake with stick.
Sorry for the long post, but I've seen this sort of thread several times before, and most of the people who comment have never set foot in the woods in their life.
However, I do recommend at least a .357 magnum. A testosterone laden buck is almost as dangerous as a meth-brained junkie, and a .357 hollow point will generally do the job on both.