To maximize your time, take a taxi, not the train. Taxi will take you about 20 minutes to the center and cost you 29 Euro. With the train, you could be standing on the track waiting for 30 minutes - a waste of your precious time. Personally, I always use red cab from the airport - they are waiting for you at arrivals. You must book and pay for the fare online and in advance. Go to www.red-cab.at. To get back to the airport, take a taxi as well, if you think you know the time and where you will be, book with red cab again.
Once in the center, assuming you will have 1-2 hours, I would have the driver drop you as close to Stephansplatz as possible. Look at the cathedral, walk down the Graben, turn left on Kohlmarkt where you will have a view of the Hofburg. Turn right on Herrengasse and have lunch/coffee/cake at Cafe Central. Walk down Herrengasse back towards the Hofburg and head towards the Opera. At the Opera take your taxi back to the airport.
I want to comment as well on the directions given above - there is no "yellow" line in Vienna. People won't know what you are talking about. I believe what the poster is referring to is the U3 line (which is color coded orange, but no one calls it the "orange" line).