There are really only two trains which serve Orlando from the Northeast - the
Silver Star and
Silver Meteor. Each follows a slightly different route from New York to Florida, but both serve Philadelphia and all Orlando area stations (Sanford, Winter Park, Orlando, and Kissimmee). The
Meteor is marginally faster (about a 19 hour trip from Philadelphia) and departs every evening from Philadelphia; the
Star gets to Orlando around noon after departing the previous afternoon. There is a third NY - Florida train, the
Palmetto, but the closest station it serves to Disney is Winter Haven.
The other trains which show up on the Amtrak website all just connect in Washington to the trains noted above, and since those pass through Philadelphia anyway, there is usually no reason to make a D.C. connection.
It is a very comfortable trip, even more so if you reserve a sleeper. The trip generally seems shorter than it really is (it helps that you are asleep about eight hours of it). The train is faster than driving (with an overnight stop) and MUCH more comfortable than air travel (and it's far, far more civilized!). On the train you can get up and move around whenever you feel like it, with a dining and lounge car (and restrooms) right there.
If you are completely new to long-distance train travel, you might consider tracking down a copy of the book
All Aboard. by Jim Loomis. It's fairly accurate and serves as a good introduction for the new passenger. Also, request a copy of Amtrak's Travel Planner and a current timetable (both available In Philadelphia and other stations). On the web, you might try:
http://www.on-track-on-line.com/amtrak-tips.shtml
and
http://www.amtrak.com/trains/silverservice.html