Overall Pinwurm has given you great, accurate advice about neighborhoods in the area. I’d just add a few things related to car ownership, since you mentioned it in your original post. Snow isn’t that much of a problem. There will only be like 5 days a year on average when you can’t drive because of snow. A car is a pain in the ass, because most places won’t have a driveway, but I wouldn’t want to live near the end of the B or C line without one.

BC has huge parking garages in the middle of campus and prices are fairly reasonable for grad students, (prices are tiered—they are crazy expensive for undergrads, but like 1/5 the cost for grad students) so I don’t think it’s crazy to have a car. BC is at the end of the B and C branches, and these lines are slow anyway. It can be a long wait for trains, and there’s also frequently maintenance on the weekends. It’s really hard to do things like grocery shop without a car, and the T will only bring you into and out of the city, so if you want to do something in the suburbs it’s practically impossible. (There is the commuter rail, but you would spend nearly an hour just getting to it before you even start towards your destination. The trains are infrequent and only serve a few communities and in most cases you’d need a car to get to your final destination once you leave the station.)