Get on the tollway near the airport, and latter the Indiana tollway. Tell the rental co. you'll be using the tollway. With the rental car transponder you don't have to stop at the Illinois tollbooths, but the tolls will appear on your rental bill.
I294 to I94 to I90
Locals skip the Indiana tollway by exiting I94 at US20 and then IN 2, but for a visitor that probably isn't worth the extra navigation steps, especially at night. (GPS or Google Maps may direct you this way.)
The connection between I94 and I90 is a little tricky. I'd check the maps for details, so the signed turns (and/or gps) don't take you by surprise.
Depending on where your are going in South Bend, you might want to take the US31/20 beltway around the west/south side.