Unless you have oversized/odd-shaped luggage or more than two "checked" sized luggage per person, Amtrak is very generous with its luggage policy. Just put your luggage in the racks. There is also carryon storage above the seats like an airplane too.

If you are doing Northeast regional, I strongly suggest booking business class. The free non-alcoholic drinks and assigned seats are worth the cost (left side is better for views going south). If doing Acela, it's a whatever there.

IMO, the Acela isn't worth it for Boston<->NYC. Time savings on the Acela is pretty negligible relative to the NER and cost. If you were doing Boston<->DC or Philly, the Acela is definitely worth it.

At least for South Station, I would arrive no later than 20 mins before departure. Gives you plenty of time to figure out where you need to go and get comfortable before the train departs.

For Moynihan Train Hall in NYC, I would say 45 mins before you leave. It's a much larger station and there are a lot more people hoping on/off, so boarding can take longer.