As you are coming in eastbound on I-44 when you get to I-270 take I-270 south to I-255. Then you can take I-255 across the state line into IL and catch I-55 at Exit 11. If you want to catch I-64 towards southern Indiana then the I-64 exit is 15 miles after crossing into IL. If you want to take I-70 to Indiana then you can catch it about 10 miles after getting back on I-55.
You'll avoid a lot of traffic and congested exits in St Louis and Metro East area. Depending on the time of day I-255 is almost deserted. The only tricky exit will be when getting back on I-55 which signs toward Chicago. After taking the exit off I-255 and you're on I-55 you'll need to get over 2 lanes to your left. The first lane on the right soon exits off I-55 into Collinsville. If traffic is heavy on I-55 don't hesitate to make the move 2 lanes.