100% you should get Business Class, more room in your seat, quieter than coach in general, plus free non-alcoholic beverage. If you want to get any sleep that is. Technically the NE Regional is not really a long distance train, so the coach are more like commuter class seating as opposed to trains like the Lake Shore Limited whose coach class is more like the NEC's Business Class.
As far as the station, just show up about 30 minutes before departure with your ticket ready. Like the others have said, no security checkpoints, just go to the correct platform when the train is announced. I have been to Providence's station which is small, you will be fine there, and when leaving NPN, just look around and get a scope of what to expect when you are leaving town.
Bottom line, upgrade to Business Class or you probably wont sleep much. Oh, and bring a pillow and blanket if you can!