Luggage is not a problem on Amtrak. Their site may say no checked baggage but that just means they don't check it in for you, you have to carry it on the train yourself. There are spaces at the end of the cars to leave your luggage and the overhead bins are larger than on airplanes.
Since you'll have the luggage, I'd suggest getting a Redcap at the stations to help you with the luggage. You just give them a tip and it's good because it usually always gets you to the train before the mad rush. You can search on the NYC and Boston forums and will get several results about this. Train's much better than bus in my opinion, more expensive but reasonable especially if booked further in advance.
A side tip, a day or so before you're due to get the train, make a habit of checking the Amtrak.com site to see about any delays or track problems so you can plan accordingly. I only mention this because there was a power outage that affected Amtrak last month and resulted in some pretty long delays and cancellations.
It depends entirely on your budget. A bus can be had for $20/person while the train will be $50+. The train is much more comfortable and takes less time because there is no traffic.
If you do decide to go by train ( better idea) make sure you book your ticket immediately. The closer it gets to the departure date the more expensive it gets. Try making believe you are going in one or two days and look at the price -:)
The regional train is about 3.5hrs from memory.
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