Upvote:0
I have lived in Philadelphia for 3 years and travelled on Amtrak quite a few times. You definitely are allowed to bring suitcases on the train. As @Jagular pointed out, the "no checked in luggage" refers to the fact that you cannot check the suitcase in the hold, as you would on an airplane - instead you will need to take it into the train car yourself. There are overhead racks for smaller items - you should be able to put your backpack there. A suitcase will definitely not fit there - but there are luggage racks at the end of each car, where you can easily put your suitcase - I have done this before.
Upvote:2
You can bring your suitcase on the Amtrak train. There are overhead bins (or racks on some trains) and an area at the end of each car for oversize bags. Unless your bag is the size of an old steamer trunk, you should have no troubles.
When they say "no checked baggage", they mean you have to handle the bags yourself.