I took the California Zephyr on my honeymoon nine years ago, and I second the recommendation above. The scenery is the best on Amtrak.My wife, not at all a railfan, had a wonderful time.
Certainly you should get the deluxe bedroom, which has a double bed for a lower berth and a private restroom with shower (very small but usable).
The trip takes two nights and two days, leaving Chicago at 3 pm and arriving Oakland, CA at 5 pm on the second day. You might want to break your trip at some point (we did at Grand Junction, CO) and do something else for a few days (dude ranch?), then rejoin the train for the rest of the trip. Two days on a train is a long time, especially if you're new to it.
There is full dining service (the food is actually pretty good) and a "sightseer" lounge car with big windows (you'll want to grab seats there before the train leaves Denver on the first morning out -- the climb into the Rockies is utterly amazing).
When you leave Chicago, you'll cross typical Midwest farm country until it gets dark. The second day you traverse Colorado, and the scenery is wonderful the entire day. You'll pass through Salt Lake City late in the evening, and cross the Nevada desert at night. The third day begins at Reno, NV and includes the High Sierras.
Be prepared for the train to be late. It probably will.
You can arrange car rentals at many Amtrak stations. If there is no rental counter in the station (there usually isn't), they will come get you or pay taxi fare.
Have a great trip!