If you end up not wanting or not buying a firearm to backpack with, I would suggest a large bottle of bear spray.
Being an avid backpacker for the past 5-7 years, I have read a lot of personal accounts as well as other info about bear spray and it has done the job in most situations.
I always carry a large bottle on my hip when backpacking, whether I am out for two nights or 2 weeks. It's easily accessible, sprays about 20-25ft, and I feel comfortable having it instead of a gun...even though I can't carry a gun in my state, backpacking or not.