Caliber debates are endlessly entertaining, but in fact anything between .22 rimfire and .44 mag is perfectly acceptable for woods cary depending on your location and needs. .22 rimfire works best for folks who want to harvest food, and the .44 is a good choice for folks who don't want to become food. Of all the handgun/caliber combinations I think the Glock 20 in 10mm is the ultimate balance of firepower and shootability, but that's just my preference and I don't disparage people who choose differently.
Bullet selection is often more important than caliber selection. It's the bullet that does the work, after all. A .38 special loaded with 125 grain hollow-points won't go through a marmot from the wrong angle, while the same .38 special loaded with 158 grain hard-cast Keith bullets will out-penetrate a .45 ACP 180 grain hollow-point...an important consideration if furry things need to be shot.
Physical stature also plays an important roll. My wife is one of the toughest people I've ever met, and she has a level of athletic strength that has to be seen to be believed. But she's very small and has had multiple hand injuries. She can shoot a 9mm much better than a .40, (which is pretty common even for large people without hand injuries). Going bigger than 9mm, regardless of the reason for carrying a handgun, would be counterproductive for her.
As others have pointed out, the caliber is of little consequence if you can't hit the target. Lots of folks fancy themselves gunslingers because they have a dozen or so handguns, or because they cary a pistol some of the time, or because they read gun magazines cover to cover, but being able to really shoot a pistol is a fantastically different thing.
Anyone who considers themselves a pretty decent pistol shot should go shoot a Steel Challenge and report back. It's amazing how people crumble under the pressure of a timer and an audience...pretty low (negligible) stress compared to any situation where a handgun is actually necessary to save yourself, or even feed yourself.
It takes thousands and thousands of rounds to be proficient with a pistol, so cost of shooting should definitely play into caliber considerations. If being charged by a furious grizzly or enraged bull moose, I'd much rather be standing beside a fellow armed with a 9mm that he runs 5,000 rounds a year through, rather than someone with a hand-cannon they'd only shot a couple hundred times. A crack shot with a hand cannon would be best, but such a person is beyond rare.
Paring caliber with a specific handgun is another factor all together. Aside from the bargain brands (Taurus, Kahr, Kel Tec, etc.) all the major brands of handguns are pretty much as good as the next. Glock, Sig, Springfield, Ruger, S&W, H&K, Colt, Kimber, etc...pick what you like. Much more important than the make, and even more important than the ergonomics, is the SIZE and WEIGHT. Too small and you can't shoot it accurately; too big and you won't cary it.
I love my Glock 20 in 10mm, but you really have to want to cary a gun to pack it around. It's not an insubstantial amount of weight, though it's half the weight of the average .44 wheelgun. The Glock 29 10mm weighs a little less, but you give up so much in ergonomics and accuracy that it's a poor compromise. It's too bad Glock doesn't make something in between.
The 11 ounce S&W .357 mag is the only gun that goes everywhere with me, and that's because it's 11 ounces. It's the definition of "any gun beats no gun", and I cary it simply for that reason. I sure wish they made a six-shot version with a 4" barrel, coming in at around 16 oz. That would be a great woods gun.
Another super woods caliber is the .22 WRM...more energy at 100 yards than the .22 LR makes at the muzzle and negligible recoil, plus the ammo doesn't weigh much. Unfortunately the handguns made in that round are either close range "defensive" weapons, or heavy-for-caliber revolvers. Not much point in carrying a .22 WRM if a .357 weighs about the same. .22 WRM is another round that would be great in a 4" revolver made from scandium and titanium, but as of yet I think they only make it in a 2" barrel. I guess people who walk the woods are a small portion of the handgun buying market.