As one who has shot through a lot of windows on Amtrak, my experience has been to not use any filters. The Lexan they use on the windows doesn't seem to have a consistent thickness and/or an uneven level of stress inside the window. The end result is that with a polarizer on, I've ended up with what looks like 'stress swirls' in the image. I've also had shots where one side of the picture is noticeably darker than the other side, or diagonally 'split'. Of course, I didn't notice the problems until I got home and had the pictures on my computer screen.
However, if you are riding a tourist train like the Durango and Silverton, I suspect they have real glass in their windows, so a CPL may or may not make sense.
Shooting from a moving train always presents a problem as you have to 'see' your picture, frame it in your camera, and shoot all in 2-3 seconds. The lighting is ever changing as the track doesn't run in a straight line for long in the mountains. So, one minute the sun is on your left, and a minute later, it's behind you, or blocked by a mountainside, etc. For this reason, shooting in full manual mode only adds to the difficulty of getting a good shot in the second or so before it 'disappears forever' in an ever-changing landscape. I've had good luck shooting in Av mode somewhere between f8 and f22 for good DOF with an ISO speed fast enough to consistently get the shutter speed above 1/100 to freeze camera motion blur. Faster than 1/125 is preferable. Obviously, if shooting into a shadow area, crank the ISO a bit or open the aperture a tad to get a good exposure while still maintaining a fast-enough shutter speed.
As for not getting reflections from the inside of the train on the window, perhaps the best solution is to have the lens hood in direct contact with the glazing. Also, rarely do I ever shoot exactly 'square' to the window as I'd end up with my own reflection in the image. Having a roomette and having the room lights off and curtains to the aisle closed helps considerably to cut down on the reflections. If your preference is standing in the vestibule, remember to keep a 3-point contact at all times...2 feet + hand gripping something, or 2 feet plus leaning against the wall. Suddenly rough track or a quick stop can put you on the floor if your feet are the only contact with the car you have. If you're in a Superliner vestibule, remember to keep the windows closed for safety reasons (passing trains are sometimes less than 12" apart, and I've seen an open trailer door (intermodal) hit the side of the Amtrak car I was riding in!). The vestibule affords opportunities to shoot on both sides but restricts the amount of available 'pre-planning' of a shot due to the horizontally small windows in the doors. Also, if you are closer to the front of the train, bears, cougars, and other large wildlife usually don't start running from the train until the locomotives pass, so be on the lookout and ready to shoot in 'full point and shoot' mode, no time to change anything.
Most of all, don't get so wrapped up in trying to get a zillion shots in 2-3 hours that you don't have time to simply watch out the window and enjoy the view. For what it's worth, I've got a cross-country Amtrak joyride coming up in 4 weeks and will be doing a lot of the same.
Sit back and relax.
edit: by the way, bring LOTs of memory card space. The last thing you want to have happen is to run out of memory (or battery power!) just as you get to the 'really good part' of the scenery. Back in the '80s, I went cross-country in Canada and ran out of film on the return trip on a different route!