It's great that you're thinking about running! If you run as an independent, you will not win or even come close to winning. For state rep seats, most voters just vote the party label because they don't know the candidates. Grafton County, even rural Grafton County, can be pretty Democratic, and this will be a pretty Democratic year. You might want to consider primary-ing the incumbent Democrat if your district leans Democratic. If you do want to run as a Republican, talk to Omer Ahearn of the Pemi-Baker GOP or Mike Long of the Upper Valley GOP or... somebody in Littleton, if you're up that way. Pretty much the Republicans around here are thrilled to have anyone decent to run, even if you're a libertarian.
Promotion... the more, the better, the closer to election day, the better. Sending a mailing is probably the best way to reach your voters in a large, rural district but can be expensive. Talk to the NHLA (nhliberty.org) about financing.