Hi,
Per the MBTA website, the parking lot is 70% filled to capacity, while 30% of spots are not filled. Stoughton is a working-class town where not everyone works in downtown Boston, and so its parking lot probably isn't super-crowded like some of the wealthier towns where most folks commute to downtown Boston.
The area where the Stoughton MBTA lot's located is a bit gritty-- wouldn't call it unsafe, but certainly not gentrified. Looking at the MBTA schedule, there's not that many rush hours trains from Stoughton to downtown, so it may not mesh well with your school schedule.
You may want to consider finding a rental house in Westwood near Islington station if possible--many people walk to that station, and you can also get there from NESL via the subway and bus (Orange Line T to Forest Hills, then the #34 bus will take you to Westwood).
MBTA Commuter Rail > Franklin Lines Schedules and Maps
The town of CANTON also has multiple MBTA stations with frequent service, and if you can afford a rental there, would probably also work better than Easton.