Trenton does not have checked baggage service. At Philly and Boston, there is checked baggage service, but it can take up to an extra day (as there's only one train that carries it, and it runs overnight.)
That said, standard-sized checked luggage can be carried onto Amtrak and stored in a luggage rack, available at the end of each train car. Each one of those does count as one of your two pieces of luggage per person. Generally speaking, you can bring two pieces of luggage and then two smaller bags (think backpack, purse, etc.) and still be within the carry-on policy. I'd highly recommend that unless you have a lot of luggage or extremely large luggage.