I've done a ton of camping an hiking in the northeast (NY, NH, ME, VT) although I now live in the southeast.
I second the motion that your biggest worry is 2-legged predators rather than the four-legged variety. Learn about how to handle cooking and food (bear bags, etc.) if you'll be in the backwoods and don't do stupid stuff like eat bacon in your tent and you'll be fine on the animal front.
I'm not a big glock fan, but a Glock 26 works nicely for me. Relatively small and light, and stands up to whatever abuse you throw at it. Plus it's already ugly so you can't really make it any worse.
Do be aware that many hiking and camping opportunities will cross all kinds of public, private, federal and state lands, and the laws can be confusing. At least in the northeast, much of the forest is a bit "crowded" and many yuppie hikers are against firearm ownership, so you probably don't want to have target practice at camp.