As of late it is not possible to start a marijuana business in the state of New Hampshire. Only certain center called Alternative Treatment Centers are allowed to give out weed to those that need it. This may change in the future as the laws are after all still evolving.
Fairly recently, New Hampshire issued licenses for several alternative treatment centers to produce and distribute marijuana according to newly passed laws on medical marijuana use. As for starting your business, unfortunately as of this moment, New Hampshire is not issuing new licenses for centers. You’ll have to keep your eyes open and perhaps try to get involved with local politicians and wait for policy to change or more licenses to be issued.
Right now New Hampshire is not open to applications for licenses to start a dispensary or any other marijuana related business. Current dispensary have had a hard time opening or operating due to hurdles at state level. It has gotten so bad that medical marijuana patients have ventured out of the state to acquire the medical marijuana. For the future the best thing you can do is ensure you have liquidity assets in the 100k-250k and a business plan, those are two major licensing requirements for almost all states.