What is the best or most reasonable way to travel between these airports? I have international flight in/out of O'Hare and will probably take domestic flights on SW Airlines from Midway. Thanks for any advice.
Michael hit the nail on the head. Traffic can be a nightmare so I would go with public transportation-Blue line downtown and transfer to Orange line to Midway. Good luck!
One of the easiest ways is to simply take the train. They are color coded to be easy to distinguish. If you take the BLUE line to downtown Chicago, and then transfer to the ORANGE line leading to midway, that is the fastest way without having to drive. Its about a 40 minute to 60 minute ride on the train. Driving can get tricky if you don't know how traffic will be (which no one really knows for sure especially if there are accidents that stop traffic).
UberX if money is no issue. It will be like $30/40 ish depending on traffic. Best way is to travel through trains/CTA
I agree with Michael's recommendation for the train, but we should amend the answer to say that you need to plan on 2 hours to make the journey as it is about 45-60 minutes to make each leg of that train trip: an hour max from MDW to downtown, and an hour max from downtown to ORD.
As such, even though I usually prefer the train, I'd make a strong recommendation to take a shuttle between the airports which you can find here or hoping a cab. Depending on the time of day, the drive is generally around an hour, particularly in the afternoon as traffic up toward O'Hare on 294 is surprisingly absent that time of day.