If you don't want to take the bus, DEFINITELY go Newark Penn Station ("NWK") over the EWR rail station. On top of the EWR rail station requiring a transfer via the slow-as-molasses AirTrain AND having less frequent service than NWK AND lacking the PATH option, EWR-NYP also costs $8-9 more each way than NWK-NYP.

One other train option to throw into the mix is the Newark Broad Street train station. There are some NJT trains to NYP that stop there but don't stop at Newark Penn ("NWK"), and if you're taking something like Uber/Lyft to get from your hotel near the airport to the train, Broad Street is probably a similar ride to NWK. That said, train frequency is significantly higher at NWK than at Broad Street (and NWK has a bunch of food and coffee vendors and the like, whereas I'm not sure if there's much of anything at Broad Street) so unless there is a big gap in the schedule at NWK that is filled by a train at Broad Street, I'd still recommend going to NWK.

If you specifically want to go to GCT and not NYP, the Newark Airport Express bus from the airport will provide a one-seat ride.