You will love the Zephyr! There really isn't a "best" side of the train because there is incredible scenery on both sides of the train. Westbound, I'd recommend grabbing a seat in the lounge car right after you leave Denver and staying there until lunch time - that is when you climb up and go through the Rocky Mountains and there is so much to see you really want to be in the lounge.
I have a standard carry-on-size suitcase and it fits nicely on the "step" in the roomette next to the seat. I like to keep it in the room with me for easy access.