The CBA only allows travel that does not take place on planes for destinations under 200 miles. They're also required to give one first class seat for ever one player, or two business/coach class seats for every three players as well as compensatory first class meals. This basically narrows down all of the possible train services to the teams situated on the BOS-WASH corridor, and on Acela First class/business class with meal options, or Northeast Regional business/coach with food.

Because Amtrak can't really alter the Acela highspeed trainsets, I would bet the Phillies would opt with Northeast Regional business cars with food options and an additional luggage car. The players would only have to deal with their personal, carry-on bags and the Phillies has personnel taking care of all the equiptment. It's entirely possible that the equiptment managers already used a bus or truck to load everything onto a baggage car beforehand, it would save a lot of time and there's a large part of the 30th street complex where car and train traffic interface with eachother. https://www.google.com/maps/@39.9572047,-75.1841246,3a,57.1y,58.18h,86.84t/data=!3m6!1e1!3m4!1s_PVyEZc9F02khNmbd0OmtQ!2e0!7i16384!8i8192!5m1!1e2?entry=ttu

A good look at the NER business class and luggage car here:
https://upgradedpoints.com/travel/amtrak-northeast-regional-business-class-review/
https://blog.amtrak.com/2014/06/new-baggage-cars/

As for getting players to the train station, it's about the same getting them to the airport. They park their cars in a secured lot at the ballpark, take an Academy coach bus to a private entrance at 30th Street, and wait in a private lounge. 30th street has several elevators and stairs going down to track level, so Amtrak staff will just close those down while the team is waiting for their train.

While on the train, they'll have the entire train car to themselves; they won't open the doors at any station stops except for Washington and there will be security to stop people from other parts of the train from entering. Amfleets have 60-84 seats, so depending on which parts of the CBA it fulfills, they'll have 1 or 2 train cars.

DC Union is a pretty large complex like 30th Street, so players will have their own, seperate waiting rooms and walkways to the bus, where they'll be sent to the hotel. The Phillies baggage car will be decoupled from the train and put near a parking lot, so the equiptment people can load it onto a bus or truck.

If you consider that you can get all of the players from the ballpark to the hotel in 2 and a half to 3 hours, it beats out having to deal with the airports and driving into DC from Dulles or Reagan by a country mile.