The Metra Electric Line is the only train that will take you to McCormick Place.
The nearest station to you is 147th, just south of Halsted, where I've parked many times, but my car was stolen from that lot so that's up to you.
I would suggest you take 294south (from Cicero) and exit at Dixie Highway. Turn right on Dixie and in a block you'll be in front of the Calument train station, it's a huge parking lot on the left, you can't miss it. Parking is $2 in bills or quarters. If you stay on Dixie, it will eventually split at a viaduct. Go straight (don't go through the viaduct) and you'll see the Homewood station on your left before you hit 183rd. Parking there requires $2 in quarters!
Here's the schedule:
http://metrarail.com/Sched/me/me.shtml
You'll need the Sunday In & Outbound.
**Just keep in mind there are two train lines between you and the Metra Electric (University Park) trains...the South-West which services Palos to Union Station, and the Rock Island which goes to LaSalle...those trains won't stop at McCormick.
Used to live in Homewood, wife works in Palos.