Even though O' Hare is a far nicer airport in a better part of town, I personally prefer flying in to Midway. Just recently, O' Hare was recognized as being the worst in the US for delays. I have never had a problem with delayed flights out of Midway. The 'El" station is right there at the airport(both stations have a station). You will see signs throughout the airport directing you to the station. Check out www.transitchicago.com for more information on the 'El' stops.
Lennox Suites was an alright place to stay. The rooms are bland and generic but the location is unbeatable. Rush street has many wonderful bars and restaurants. If you can upgrade to a one bedroom suite it will be much better. Their 'Studio Suites' is essentially an ordinary, nondescript room with a scuzzy closet sized kitchen. Either way, you will have the advantage of a premium location.