1.) CAPITOL LIMITED to Chicago and the CALIFORNIA ZEPHYR to Sacramento. The California State Railroad Museum, Old Sacramento (the starting point for CP construction through the Sierras), and a motel are within easy walking distance of the Amtrak station.
1b.) Three options from Sacramento (or from Oakland / San Francisco): A.) Ride the COAST STARLIGHT north to Seattle and return to Chicago on the EMPIRE BUILDER; B.) Go south to Los Angeles on the COAST STARLIGHT, the CAPITOL CORRIDOR, or PACIFIC SURFLINER. Return to Chicago on the SOUTHWEST CHIEF (a connection to the Grand Canyon Railway is available at Williams Jct, AZ); C.) From Los Angeles, ride to New Orleans on the SUNSET LIMITED. Return to Chicago on the CITY OF NEW ORLEANS.
2.) You can get off and on but an itinerary has to be set before a trip begins. Amtrak posts package deals / promotions at www.amtrak.com.
3.) The end of this year is fast approaching. I'm not certain how far reservations can be made for 2016. Ask Amtrak.
4.) My personal favorites are Summer and Fall, when Colorado is aglow with golden aspen. Winter (other than heavily-traveled Thanksgiving and Christmas) is an economical time to travel. Snow in the West provides magnificent sights.
5.) Before contacting Amtrak or AAA, get the current Amtrak System Timetable and Amtrak Vacations. Those two booklets provide a LOT of information. They are available from Amtrak or at Amtrak stations. Read them first.
6.) Don't assume private varnish is too expensive. Some trips are run for short distances and for the general public. I think at least one account and photos are posted on the Forum, probably under Real Trains.