First off- I'm sorry for your loss. I have several of my grandfathers guns that have a lot of childhood memories attached to them and they are very dear to me.
You have access to an outstanding training facility. Sig Sauer Academy is right in Exeter, NH. It is fantastic, and state of the art. Take the money you saved not having to purchase the guns and take this:
Courses for firearm, self-defense and law enforcement training.
or this:
Courses for firearm, self-defense and law enforcement training.
It will be $195 well spent. Not only will you get answers to answer all your questions about the legalities, you will also get safety and skill training as well as satisfying the training requirement needed for many other states should you want to get your CCW there. They offer many other advanced courses as well should you decide to further your skill/knowledge.
You DO NOT need a license to open carry a firearm in NH but you DO need one to have it loaded in your car or concealed in any way. I highly recommend you get your permit- NH is a shall issue state and you should have no problem with your local Chief of police.
(some smaller towns do not handle CCW's so you will have to contact the State Police at 10 Hazen Dr. in Concord)
Just because you can carry does not mean that you should. You need to fully understand the responsibilities and legal ramifications this right carries with it, as well as being properly trained so you do not injure yourself or someone else. A training course will allow you to make an informed and confident decision about whether carrying a handgun is for you.
I applaud your desire to exercise your rights and to be a responsible, armed citizen. Good luck and enjoy your treasures.