Your criteria constitute a tall order. As far as I know, there are very few towns without police, and those are very far north. Dummer may be one of the few towns without police, but that is in the middle of nowhere. Also, if you want to do a lot of shooting on your own property you're best off north of the lakes region, although you may also make it work in the southwest part of the state. The problem isn't finding the land, the problem will be noise complaints from neighbors. Luckily, there are some great gun clubs all over the state, but especially in southern New Hampshire. I'm thinking of Pelham F&G, Nashua F&G, Londonderry F&G, and many others. I live in Manchester and I belong to several clubs - convenient shooting is not a problem.
Politically New Hampshire has gone 'purple' over the past 15 years or so. Do a search for "Red Blue Map New Hampshire 2016" to get a sense of where the more conservative towns are. If you're more interested in solitude and elbow room, go north. If you want to stay under the 3 hour mark for your Boston commute, then stay south of Laconia. I haven't done a lot of exploring in the southwest part of the state (Fitzwilliam, Winchester, Troy, Swanzey) but I get the feeling that this might be the state's best kept secret for quiet living not too far from Boston.