Going from SLC east, head to the observation car as soon as it's light out, if you want to see the mountains (which you should). The observation car will fill up fast. Also, the train will seem half-empty when you get on, but will start filling up as you get to the ski areas west of Denver.
Some people have a lot of trouble sleeping in coach, others have no trouble. You probably want to bring sleep mask, earplugs, the usual things you would use for sleeping on an airplane or a bus. Others recommend clothespins to make sure the curtains stay shut! If you use a CPAP machine, *you can actually plug it in on the train and use it*, which is awesomely superior to other methods of overnight transport.
There's usually enough time to step out on the platform and look around a little at Grand Junction (two former classic railway station buildings, sadly disused and locked up) and Denver (Union Station) -- make sure you get back on well before departure time at Denver, though. At GJ they'll usually yell at you to get back on when it's time.
Amtrak often runs an hour or two late; expect that. More than that is unusual, though not unheard of.
Breakfast is reasonably priced, much nicer than what you can get in the cafe, and oddly, usually not very crowded. Amtrak takes reservations for lunch and dinner; breakfast is first-come first-served. If you eat breakfast normally, I would definitely get breakfast in the dining car both mornings. Dinner can get quite pricey.
Amtrak's menus are here:
http://www.amtrak.com/servlet/ContentServer?c=Page&pagename=am%2FLayout&cid=1241305537990
Meal times in the dining car are here:
http://www.amtrak.com/servlet/ContentServer?c=Page&pagename=am%2FLayout&cid=1248539615772
You can decide in advance for each meal whether you want the dining car food, the cafe food (convection-oven reheated fast food material, though I actually quite like the hot dogs), or whether you want to pack your own cold meals.
When comparing prices, please do note that the roomette price includes meals in the dining car; in your case they'd include breakfast, lunch, dinner, and breakfast and lunch again. The roomette usually still costs more than coach + meals, but it depends not only on what the roomette charge is on the day you're travelling, but also on what you're planning to eat! Roomettes are sometimes relatively cheap from SLC to CHI, though the price depends on how close they are to sold out, just like airline pricing.
SLC to Chicago is a long trip, longer than my first trip in coach. Try it out, see whether you like it. A number of people find this trip to be too long to do in coach, others think it's fine. Almost everyone says it's a very nice trip in a roomette. It's certainly slower than taking an airplane, though.
If you decide that you really don't want to spend two nights on the train, it's possible to take the train from SLC to Denver and an airplane from Denver to Chicago. There's a "SkyRide" bus direct from Denver Union Station to the Denver Airport. I don't particularly recommend this (I don't fly), but it's possible, and I notice that most flights from SLC to Chicago make you change planes in Denver anyway. It may also make it cheaper to get a roomette (SLC-Denver on Amtrak is much less busy than Denver-Chicago, and so has lower prices).
Just for completeness, it's also possible to fly from SLC to Denver and take the train from Denver to Chicago, but then you miss all the scenery on the train (overnight most of the way) and it's probably more expensive (Denver-Chicago on Amtrak is busier than SLC-Denver and so has higher prices).
Anyway, that's probably more information than you wanted!
