A few notes from a Seacoast NH native -

MHT isn't really much closer to Wentworth by the Sea than PWM is. But if it's cheaper, so be it. Otherwise, as noted, the airport in PWM is (relatively) close to the train station.

Boston North vs. South Station, if you are not immediately transferring services, doesn't matter. North is just Downeaster, some commuter services and some subway lines, where South is all other Amtrak, all intercity bus lines and some subway lines (including to Logan), but both are at opposite ends of downtown and are easy access to equal numbers of attractions and the like.

C&J bus from Portsmouth is located a bit outside of town, so you'd still need a taxi or the like to get there. This is the same location that Amtrak is denoting "PTS." If it comes down to buses, you can also take a Greyhound (pretty clean and easy in this neck of the woods, unlike other parts of the country) from downtown Portsmouth.

You might look into the local bus from Portsmouth up to the Dover Train Station. http://www.coastbus.org/schedules.html Don't be fretted by local buses if you normally are...there will likely be no one else on it.

Have fun...Portsmouth in summer is the best there is.