Bank of America is almost at every corner you turn. Citizens Bank is also a popular bank, but that bank does not appear as frequently, and from my own experience, I like Bank of America much better.
That is similar to what I am doing. I go to a school nearby Northeastern, but I decided to live outside of Boston to save some money. I live in Somerville, MA nearby the red line, and the commute can be anywhere from 35 minutes to a little over an hour (during rush hour), also depending on how lucky you get with the trains. For the most part, the commute isn't so bad, especially if you pick up the Globe. The only thing to really keep in mind are when the T (the train) stops running after midnight. Cambridge is also a good place to live, but prices will depend on where exactly you're looking. Brookline would probably be an easier commute, and you'll be around a lot of BU, BC, and COF students.