This is an easy one, given your arrival into Midway and subsequent itinerary. (Why did you mention O'Hare though?) Spend the night near Midway, and pick up the car there in the morning. Union Station is in exactly the wrong direction for your trip to Indiana. Plus, the trip on the El, with luggage, after flying transatlantic, would be rough, not to mention your having to negotiate the bowels of Union Station just to make it up to the street and daylight. I still get lost down there.

It isn't that bad getting over to I-90 from Midway. You can either head slightly back up towards town on I-55 to connect to I-90, or make your way due east on surface streets straight to I-90.

The only reason I could think of to steer you to your other option, would be if you actually wanted to do anything that evening of your arrival. There is NOTHING to do at Midway, while Union Station is in an interesting corner of downtown.

Since you are eventually departing from Union Station after dropping off your car, it does make sense however to drive all the way to the Avis office you mentioned. Going back to Midway, and then taking the El to the Station represents a lot of unnecessary and even hellacious complication. The I-90 practically deposits you at Union Station, although I might advise you to take the Roosevelt Road exit (east) just slightly south of where you want to be, and then head north up Canal street about 5 blocks right to the Station. This will avoid the nightmare interchange of I-90 and I-290.

By the way, I can't think of any hotels near Midway Airport! I hope you know more about this area than I.

Best regards, Joel