Others will throw in their own opinions. Here is my advice: For expediency and better scenery, get yourself up to Flagstaff. Either take a bus ( the night before ) or drive up there. ( I live in Flagstaff and can give you more info on request. ) If you are up for a pretty interesting but rather long trip, you probably know that Amtrak has not stopped in Phoenix itself in some years, because of Union Pacific downgrading the line through Phoenix. Your stop is Maricopa, 30 miles or so to the south. My friend and I went this route several months ago and boarded in Tucson. We enjoyed this route very much, but it may not be for everybody. The route from Flagstaff involves one night on the train to Chicago; the second the Sunset Limited/Texas Eagle, involves two nights. One caoch and one sleeper are detached from the New Orleans bound Sunset Limited early in the morning and coupled on to the Texas Eagle bound for Chicago. Some may find this route boring - not in our opinion. Going through small towns in Texas away from Interstate highways kept our attention.
To sum up: Southwest Chief, Flagstaff to Chicago, faster schedule, dramatic scenery through northern New Mexico into Colorado.
Runs daily: Ex. Lv. Flagstaff 4:41 am, arrive the next day in Chicago around 3:15 pm.
Sunset Limited/Texas Eagle - only runs three days a week. Leave early morning from MAricopa or Tucson, arrive 2 days later midday in Chicago. Several trains per day connecting to Milwaukee. Others will also tell you that if you take the second option, be sure to book Train 422, ( Train 421 westbound )which represents the one through sleeper and one through coach that is switched out in San Antonio to the Tecas Eagle. Otherwise, you will end up having to get off in San Antonio and wait around at odd hours for boarding the next train.
