Where are you camping and what sort of hiking are you doing?
Remember that your brain is still the most important thing you will bring.
Don't plan to get yourself out of any real trouble with a gun. You aren't going to go rambo on a gang of armed pot-growing criminals with your 6-shot revolver, and do everything you can do to avoid an aggressive bear situation in the first place... Really shouldn't be too hard 99.9% of the time in the northeast. Be familiar with how bears behave and how to tell whether a bear thinks you're food or thinks you're a threat it needs to deal with, and how you should react in either situation.
Even if you have that large caliber rifle in your hands, it's no guarantee of safety. In one study that was done that examined 269 bear attacks on hunters armed with guns, 56% of the hunters were injured or worse. Guess it's pretty hard to hit a bear charging at you at 30mph, especially when you're not fully prepared for it and the adrenaline is on full blast.
I don't mean to stir up a flame war over whether you should carry in the woods or not - it's a personal thing and it also depends a lot on where you're going and what you're doing. But I thought I would add that among my friends there is about 10,000 miles of combined hiking experience all over the USA (Appalachian Trail, Pacific Crest Trail, Continental Divide Trail, etc). None of them ever carried a gun, though they carried bear spray in some areas.
I don't carry a gun in the woods, but if I was going to I would probably get one of those sweet j-frame S&W 357's with the scandium frame... This isn't Alaska, and 2-legged critters are much more likely to be a problem than 4-legged ones. (well, that's not entirely true: There's a reasonable chance a black bear comes through your campsite at night hoping to steal your food, but the odds of being attacked by one are still very slim. Only 63 fatal black bear attacks in the past 110 years...)