One town not mentioned is Shelburne NH. It is "bedroom town" east of Gorham/ Most of the land is in the WMNF or otherwise protected from development. RT 2 bypasses most of the town so its pretty quiet. The locals are pretty active in the town. Its also about 85 miles to the Portland Maine airport which is handy for air travel. The property taxes are about half of Gorham although the houses are typically more expensive. The area is getting a slow influx of early retirees and there is an active local trail group restablishing an extensive trail network. The down side like Randolph to the west of Gorham is that everything is in Gorham, there isnt even a variety store/gas station in Shelburne. There are also minimal services, if you need fire or ambulance, they mostly come from Gorham. Its worth adding to your lists for a stop.
Randolph is a summer colony, most of the population is seasonal. The town is roughly split in thirds, Randolph Hill Road, Durand Road and the west end of town. The views from Randolph Hill Road are great but in the winter, its one of the snowiest spots in NH. Taxes are 1/3 of Gorham but house prices are high. Many houses sell privately an quickly.
The berlin gorham area is at a low point these days, but the expected influx of 400 jobs in the next 18 months and the restart of the papermill will help things along. Gorham has been a middle class vacation town, more affluent folks stay south of whites. One major plus that many hikers miss out is that north of Berlin are several major almost undeveloped lakes plus the Androscoggin River watershed which is pristene north of Berlin. The closest major airport is Portland Maine.
The Berlin/Gorham Shelburne Randolph area has the majority of the economic activity in the North Country and most of the professionals so there is going to be an economic base. Lancaster is the county seat, but its been hit hard by the loss of the manufacturing base north on RT 3.
I have lived in Gorham for over 20 years its a nuce small town, although a lot of the character of the town was lost over the years due to strip development along Rt 16 and RT 2. A big plus to some is that it has police, a viable volunteer fire dept and a partly professional ambulance service plus trash pickup. The taxes are becoming high to pay for those services so its a trade off.
I can comment much on Jefferson, not a lot of services, but good views. Plan on driving to either Lancaster or Gorham for most anything expect for gas and a couple of variety stores.
Do be aware that when looking at houses, that the regional real estate brokers tend to list houses that are desirable to out of staters at very high prices, except when the market is hot, there is considerable margin built into the prices of many homes. The brokers are quite adept at manipulating potential buyers,so dont let them convince you about making a low offer.
Feel free to PM if you want more info.