Well first off, I would work on some of your spelling there, you are going to college you know!
So the answer to your question is no, you don't need a license to purchase a shotgun in NH. Everything you need to know is here:
Frequently Asked Questions about New Hampshire Gun Laws | Free State Blogs
You would be very wise to take your girlfriend's father up on the training and hopefully get some safety instruction from certified range or instructors on the use of that shotty.
Also from your description of your new digs and the list of nice stuff you described, including that BMW, you were indeed no doubt noticed moving into there and I am pretty sure someone probably took inventory for later reference. Make sure your door and window locks work and are secure, maybe even get you a dog, oh, and good luck with your pursuit of a degree and be safe, also be aware of your surroundings at all times.
Why does this sort of remind me of this? May not be a bad idea.