Thanks guys, that's really helpful.

One further question: when I try a dummy booking on the website, the best routeing seems to be a Regional to DC, then the Capitol Ltd to Chicago and the California Zephyr onward from there. Both connections are fairly long (a good few hours in between trains). I have friends in both DC and Chicago, so presumably Amtrak wouldn't have any problem with me leaving the station for a couple of hours for breakfast/lunch/coffee then returning later on to catch the onward service.