This comes up a lot.
If you're talking about about a long term type of situation, I think a centerfire handgun for defensive use and a .22LR rifle for poaching (which is basically what it would come down to) would work OK. The .22 still isn't entirely helpless out to around 150 yards in skilled hands - as a teenager I could rountinely hit rocks the size of a coffee cup at that range with calm winds and a steady position. Add in the firepower of a 10/22 or maybe a lever or pump action and you do have something viable for self defense. It's not ideal but I have shot completely through cars with standard .22 LR 40 grain LRN so it's not to be underestimated.
For a little over $200 you can still get a new bolt action .22 LR and about 3500 rounds at Wal-mart, probably about $20 more for the package at a gun store. Everyone should have one anyhow, and at that price there is no excuse not to.

Handguns are too personal - pick what you like. For now, mine is a 9mm but a .357 would probably be more versatile. In my area, 9mm, .38 special, .357, .40 S&W, and .45 ACP are all very common. The biggest predator I could end up facing is a black bear and although the 9mm and .38 are admittedly underpowered for bear defense, I still think the 9mm loaded with FMJ would work OK because it penetrates very well. As I said, it's what I have so it's what I carry in the woods. If I had to worry about bigger predators I'd have to upgrade, probably to a .44 magnum. For my uses though, I prefer smaller full-size or mid-sized guns. They are big enough to shoot well but compact enough to carry fairly easy - decent compromise.

I'd also add a centerfire rifle - whatever works best for you. I tend to gravitate toward the full power .30 caliber rounds because I cut my teeth on them - my first rifle was an SMLE. It depends on your uses. My environment dicates something that is powerful enough to reliably kill deer or black bear (I don't hunt bear and have NEVER had a bad ecounter with one but I need enough power to defend myself against them and I'd eat one if I had to). To me, that means I personally wouldn't be comfortable with less than a 30-30 or 7.62x39 in terms of power (especially for the bear). I also like the range of the .308 but wouldn't feel at all uncomfortable if a No.4 Enfield or Marlin 30-30 was my only centerfire. For the guys who live in Alaska, they're probably going to want more gun than that, although the .303 apparently has a good rep on big animals with 215 grain bullets. Environment and availability are the biggest factors in this choice. In my area, 30-30 and 30'06 would serve very well (tied for most available), .308 is still pretty good, .270 is pretty common, and even .300 Savage, .35 Remington, and .303 British are widely available.

I like shotguns but I think they are outclassed in many ways by other choices. Handguns are better for carrying, .22 LR is more efficient for getting meat (as are snares), and a centerfire rifle will often quadruple the range without giving up anything at contact distance. Shotguns are versatile but if you have the other three, you don't need versatile because you have the right tools for many jobs.
I do admit though that it has always been easier to get game with a shotgun than with a .22. The shotgun is just more forgiving. If you were hurt, tired, hungry, shivering, it does add an extra margin in. But for the cost of two 12 gauge shells you can carry 60 rounds of .22 LR. Some guys love them and that's fine. I like them too and am planning to get another as a knockaround gun, but I don't consider them a necessity.