In order to get it, you need be sponsored by a company or an institution. After having worked for them during two years you could ask for the Green Card or Permanent Residence Card. Definitely, even if you are planning to stay here for a short while. The cost of medical care in the Boston area is extremely high. You may enroll the MIT Program or purchase any other insurance in Europe, but you must make sure the coverage your insurance is enough for the requirements your status asks.
Most newcomers spend two weeks, at least, looking for adequate accommodations.
Housing on campus is avalaible only to fully registered students, not to research staff, faculty or scholars. MIT has an Off-Campus Housing Service which maintains listings of rooms, apartments, shared apartments and houses forrent in Cambridge as well as in the greater Boston area. Anyway, we do not recommend renting any house or apartment before you have seen it. Hotel and motel accommodations are quite scarce from June through September and reservations should be made in advance.