You could do a mix of Coach and rooms to keep it affordable.
For example, ride in Coach from City A to City B and then book a room from City B to City C. Then book Coach from City C to City D. If you book the room(s) for nighttime, that will give you a decent night's sleep and access to a shower. Plus, if you're in a room during any of the meal times, that meal is included in your room charge.
For three people, I would either do two roomettes or one bedroom, depending on which option is cheaper. (I think the third person in the bedroom has to pay for their meal now, but I can't remember for sure.) The bottom bunk is the same size as a twin bed, so if two of you are small, you could share the bottom bunk and put the third person in the top bunk. The bedrooms have a private shower, toilet, and sink. The roomettes do not, but the communal bathrooms and shower are kept quite clean.
As others have mentioned, if you have a room to Chicago or from Chicago, that will give you access to Chicago's Metropolitan Lounge. It has wi-fi, snacks, and drinks along with luggage storage. It's also clean, quiet, and comfortable.