If you go through with such a scheme, your best bet is probably a bus from Portland, because that would take you to South Station, which is where you would need to catch the bus to New Hampshire. If you took the train to Boston, you'd end up at North Station and would need to get yourself from there to South Statuion, which is surprisingly inconvenient--not a big deal, but extra hassle in a trip that's already longer and more complicated than you want.
Unfortunately, public trasnportation options in northern New England are relatively sparse.
If you Google Concord Trailways or Concord Coach Lines you'll find the website for the company that operates bus service to both Portland ME and North Conway NH -- unfortunately, as already noted, their only service is by way of Boston.
They offer numerous trips each day from Portland to Boston, but the last I knew, only two trips per day from Boston to North Conway -- so I'd check the Schedules-and-Fares section of their website carefully to avoid a long wait between buses at South Station in Boston.
Have a great weekend