Been in Southern NH for about 12 years now. Lived in a number of towns from Manchester to Nashua and been in Windham for 9 of those 12 years.

I highly recommend renting for a year and driving around a bunch to learn the towns.

Given that you are from NYC and now DC, you really need to get a sense of what it will be like. NH has a lot of variety and a lot to offer in a relative small area. It's also a lot easier to go North South along 93 or 89 or 3 than it is to go east-west. Those are the kinds of things you'll learn.

One thing is that we get a lot more snow than DC and the NYC area, so priorities, like off-street parking vs a garage vs carport become worth thinking about.
Other things will be... How on grid vs off grid do you want to be? Closer to the cities you'll find natural gas and city water. Surrounding towns may be well, septic, oil heat, etc.

Feel free to DM if you have specific questions.

My wife and I went through that exact same situation about 9 years ago.

I highly recommend looking around at a large number of towns. We looked at everywhere from Nashua, Hollis, Merrimack, Hudson, Windham, Amherst, Salem, Manch. I wish we had looked a bit more east of 93 into Derry, Atkinson, Sanbornton.

Ultimately, we settled into Windham. One thing to note about schools is that there are _charter_ schools in the state and are open to all residents of the state. Buses are only for in-town kids, but parents drop from surrounding towns.

Also note that the character of the towns can vary a bit within the towns. It's a quirk I've found in Southern NH. Neighborhoods matter I guess is how I'd say it.