I should notify you about one catch regarding the schedules from STR (the airport) and ZWS (the central station): There are two lines of S-Bahn trains running on the route with a total of 4 trains per hour, but unfortunately they don't leave in 15-minute intervals but there will be two trains within 10 minutes and then 20 minutes without any train.
By the way, if you don't already have your train ticket for the onward journey, you need to buy a ticket valid for three zones to get to ZWS. If you are travelling with a companion and both of you will also be returning by S-Bahn from ZWS, it is cheaper to buy a ticket valid for 4 rides (stamp twice to make it valid for two people).
Ah, and something more: In concourse 1, there's a ticket machine in baggage claim (next to the exit), so you may even buy your S-Bahn ticket while still waiting for your luggage.
Programs: UA 1P 1MM, ICH Plat, HH Silver, DB BahnComfort
Just by the way: the S-Bahn trains from Stuttgart Airport to Stuttgart Hbf (main station) are also run by Deutsche Bahn. So, you can buy a single ticket directly from the airport to your final destination, Giengen. You can either buy it online and print it out before your trip, or you can buy it from one of the Deutsche Bahn ticket machines at the airport. (The machines can be switeched to an English user interface and also take credit cards, so this is a good option.) The S-Bahn trains from the airport to the main station leave at xx:08, xx:18, xx:38 and xx:48 and take 31 minutes for the trip.
Since the arrival time of your flight is slightly variable, as is the wait time for baggage, I would actually suggest that you buy your rail ticket at the airport. The ticket machine will actually then compute the best itinerary for you at that specific departure time, which you can also print out and take with you. It generally also includes the arrival and departure platforms you will use, and notifies you if any of your trains are so late that the connections are endangered.
Some more advice: If you are on a tight connection at central station, be sure to board the S-Bahn train in the first coach. Upon getting off at central station, walk in the direction of travel and take the flight of stairs at the very end of the S-Bahn station. After a right U-turn (and another flight of stairs), you'll end up somewhere between tracks 1 and 2 (of 16) in the station.