Good news/bad news:
Out of EDI, there's no real dominant carrier. The carriers that fly the most destinations are Ryanair and Easyjet (and like most students abroad in Europe, you may end up flying them more than you'd ever thought).
If you are going to be travelling around Europe a lot, no alliance really has the edge.
One issue to flag- for flying EDI-BOS, Aer Lingus is probably often going to be the cheapest option. You can credit Aer Lingus flights to United (50-75% on North America-Ireland, and 250 miles on some) and British Airways (reduced credit and no tier points).

If you go with Delta or United, you should make sure to use your school address, as you wont have to spend a minimum dollar amount to get elite status.