We always park at Midway Park Ride & Fly They are on 47th Street. From I-55 exit on Central and go South. Make the first left turn and it is about a block down on your left. You can also get there by going west on 47th from Cicero.
http://www.parkrideflyusa.com/mdw-chicago-midway-airport-parking/
If you sign up for their emails, you'll constantly get 10% off coupons.
I started parking there years ago when my sister-in-law was traveling. She told me when the bus dropped her at her car, they always waited for her to get in the car and get it started.
Here's how it works: You get the best price by booking on line. When you get there they tell you where to park. A bus comes quickly and picks you up right at your car. They lift your bags into their bus. The bus drops you off at the terminal.
On your return they ask you to call. I never do that. I just go outside the furthest north exit door from baggage claim and go to the 2nd island where the busses are. There's often one sitting there. If I'm waiting more than a couple minutes, I might give them a call. Once they drive you to your car they help with your bags and even put them in the car for you.
Some folks feel 47th and Central is a bit far from the airport. If you are getting to the airport from I-55, then it doesn't matter anyway.
What else? Let's see...they have some indoor parking available...I never use that. Everybody I know who parks at MDW parks here. It is cheaper than the city lot on 55th. If you park at the city lot, you have to lug your bags to the bus stop and onto the bus (I think). I signed up for their frequent parker program and get a day free for every day I park there.
Well, you asked!