^...x2 on what Matt said.
Not to discourage your alternate reg. plan, but to register in NH you'll need a physical address in state and will need to register in the town in which you've chosen to reside.
You'll need to do this in person, as NH will not do a mail in registration on a first time vehicle registration.
Now just to the left of NH lies VT, where I've read, the registration process is much simpler and can all be done by mail.