How large is your suitcase? Amtrak's carry-on rules are loosely enforced compared to the airlines. On Amtrak, "no checked luggage" means that you cannot check your bags with Amtrak (e.g. if the train has no baggage car); you can still bring them onboard and look after them yourself. The trains on the Northeast Corridor have overhead racks as well as shelves at the end of each car where you can stash your bags.
There are no intercity buses to Philadelphia which depart directly from EWR (Trans Bridge Lines only serves some Northeast and Central Pennsylvania destinations). You would need get to Newark Penn Station, where BoltBus and Greyhound connections are available. BoltBus and Greyhound will both have luggage compartments. This will, however, require a commuter train or bus connection, vehicles which will not have luggage racks or storage. The $30 or so for a taxi may be worth it, but note that you would be arriving after the start of rush hour.
Note also that the Greyhound station in Philadelphia is located near the Market East Station, not 30th Street Station. To get to UPenn you'd need to take the Market-Frankford Line from 11th Street. BoltBus goes to JFK and 30th Street near 30th Street Station, which is a longish walk to Penn, although with a large bag at night, a taxi may be a better idea. You will arrive in Philadelphia too late for the LUCY shuttle.
There is a possibility that long-distance trains that do permit checked baggage stop at NWK, but I did not check.
Directly from the EWR train station you could take an NJ TRANSIT Northeast Corridor Line train to Trenton, then connect to a SEPTA Trenton Line train to Center City/30th Street. You will not be able to buy SEPTA tickets at EWR, so leave time at the Trenton Transit Center to purchase tickets, or bring cash to purchase them on board. There is a penalty for on-board ticket sales, but you can receive credit for the difference if you are making a round trip.