Out of the 240 or so communities in NH, Durham is one of the 40 or so with the least amount of snow. Dover and Portsmouth aren't know for a lot of snow, either. I recommend anything, you will likely do fine. If you are really nervous, perhaps FWD 2WD with all season tires. If you are insanely nervous, get 2 snow tires for the front of your car. If you are so nervous that you died 10 years ago, get an all wheel drive vehicle and chains for all of your tires.
BTW, there is a bus that travels b/t a few of the Durham area communities including Portsmouth and Dover. It is low priced. There is another daily bus that goes to South Station and the airport in Boston. There is another bus that goes to NYC. Oh, and there is a train that goes from Portland, ME to Boston, MA with a whole bunch of stops, several times per day, including Durham. You don't even need a car in Durham if you can get to the bus or train station.