If you have time, and if saving money is more important than rapid transportation, you can get from the STR airport to the Marriott as follows:

Take the S-Bahn (lines 2 or 3) from the airport toward the Stuttgart city center. Get off at the Vaihingen stop and transfer to the Bus 84 at the Vaihingen train station. It will take you to Sindelfingen and goes right past the Marriott. I think the whole trip (the ticket is good for bus and S-Bahn) is only two or three zones (check at the ticket machine) and so would run under € 5 for the trip.

To get from the Marriott to the Airport (or the Messe, which is at the airport), reverse the process.

The only caveat (aside from the fact it is slower than taxi) is that Bus 84 only runs about once an hour except for the peak travel periods in the morning and afternoon when it runs three (I think) times an hour.

It's a nice property (formerly a Ramada), and has been mentioned, the lounge -- and the staff attitude -- are both great.