I flew to Israel earlier this year from the DC area. My plane to Israel left from the Newark Airport. (Return was to JFK). My departure involved taking the AMTRAK train to the Newark Airport, since I too could not just buy a one-way ticket from DC to Newark NJ for under a few hundred dollars! (train cost about $60).

The DC - Newark train went through Philadelphia's 30th St Station. No changing would be involved. (make sure you buy train tickets to the Newark Airport and not to Newark itself - I almost bought tickets with the wrong destination.)

At the train station at the Newark Airport you get on to something called the Air Train to get to your air departure terminal. The Air train is free if you have continuning-on tickets to a flight. Air Train is elevated rail cars that run every 10 minutes or so and have big wide doors and elevators. No difficulty to negotiate with a BIG heavy wheeled suitcase. The Air Train circulates all around the airport, including the train station.

I don't know about NJ Transit at all.

AMTRAK prices aren't static the way they used to be. Like the airlines, AMTRAK prices now change according to how far out you are buying the ticket. More if it's next week, much less if it's months away.

AMTRAK trains can be difficult to negotiate if you have a big suitcase and the train is crowded. Some of the cars have big spaces to park bulky bags and some don't.

--Linda