Every time I come to Vienna, I see tourist falling into the trap with the AirPort Express.
Everywhere in the airport is advertisement for the express train.
The ticket costs 14.90 Euro and brings you to the city.
If you just walk to the train station and buy a ticket for local trains (with subways and busses), you pay only 4.50 Euro. It brings you into the city and you can continue switch trains and reach your destination.