A .357 revolver, as many have suggested, may be a good choice. Revolvers are simple, reliable, and capable.

If the largest thing you have to worry about is a mountain lion (which are usually hunted by treeing them with dogs and then shot with calibers as small as .22LR), then I would suggest a semi-auto, like a Glock or a S&W M&P (or any other quality semi-auto) in a just about any common caliber (9mm, .40 S&W, .45 ACP). Modern bonded ammunition has really all but closed the performance gap between calibers. I would submit that in most of the eastern US you are more likely to have to defend yourself from 2 legged predators than the 4 legged variety and being able to quickly and accurately bring lots of well placed projectiles into play is key to surviving.

Let's face it, no matter what any legend or gun shop story tells us, anything fired from an easily carried handgun is a poor stopper when compared to a long gun. A huge majority of people shot with handguns survive. Handguns are a compromise for when we can't carry something bigger. With that in mind, I want the platform that let's me carry the most ammo, not necessarily the most powerful ammo (if the latter were my concern, I would be carrying a rifle).

My favorite woods gun for my area is a Glock 35. I like the extended sight radius and the relative light weight. I like have 15+1 rounds of .40 S&W. I like knowing that when I do my part I can keep most of my rounds on a 20 inch target at 100 yards. The .40 even shoots relatively flat with very little hold over out to 100 yards. Of course, if 100 yard shots are called for (EXTREMELY unlikely), I would rather have a rifle. However, it is comforting knowing that the platform is capable and that I have practiced at extended ranges (walk back drills).