Can anyone tell me the best public transportation from Manchester NH airport to Ogunquit ME?

Portland, ME has a jetport, which would be the best if you can swing it. There’s also Portsmouth, NH (tiny) and Boston Logan (Huge). Google the airport and click on Ground Transportation, then Google the mutual van companies.

Amtrak goes to Wells, ME which is close to Ogunquit. You can get a Hampton Shuttle mutual van from Manchester Airport to Dover, then pick up the train to Wells. Or you can glide in to Logan, and take the Hampton Shuttle to Wells. Go with the one that’s the cheapest air fare.