To your first question:
*The Texas Eagle (TE) is a double-decker train that has a lounge car with large windows, while the Lincoln Service (LS) trains are single-level cars. The viewing opportunity on the TE is better than the LS, but this is a very minor point considering you're going mostly through Illinois farmland. Really lots and lots of nothing but really large lots. :giggle:
*TE has a full dining car and a cafe, while the LS trains have only the cafe. Since the dining car serves only at set meal-times, so you could have only dinner on the TE before arriving in St. Louis, while the cafe car on both trains is open pretty much all the time, this is also a relatively minor point.
*LS trains have a business class car for a few dollars more, where you get a nicer seat, a non-alcoholic drink, and (as I recall) a newspaper. The TE doesn't have business class but you could book a sleeping room for yourself if you've got money to burn and a great desire for privacy.
*As to luggage, there's no checked luggage on the LS trains but usually plenty of place to store large bags, including a rack and open space at the ends of the cars as well as the over-seat space.
In sum, a relatively short daytime trip like CHI-STL comes down mostly to price and frequency. There's only one TE daily, but four LS trains. And as you've found, the LS is cheaper because Amtrak is trying to encourage passengers traveling CHI-STL and the stops inbetween to use the LS trains while saving seats on the TE for those going beyond STL.
As to your second question, the St. Louis station is not famous old Union Station but a new intermodal (intercity buses also stop there) station a few blocks away. The Amtrak and Texas Eagle websites show rental cars as being "on call" rather than on-site at STL station. However, there's a Budget location about a block away. Also, there's a Metrolink light rail station at the train station, and one end of the Metrolink is at Lambert Airport where there would be plenty of car rental options.