I generally carry almost anytime. I'm not too concerned with anything out in the Maine woods but it never hurts. The amount of Rabid animals seems to be on the rise and I'm usually out with at least one of my dogs so protecting them in important as well. Although they are hunting dogs and vaccinated I don't need the headache.
As for what to carry, whatever you are comfortable with. Try a lot for comfort and fit, go to some ranges and rent different types of handguns until you find one you like. After that shoot and shoot often to stay proficient.
Good luck this season from a fellow Mainer!