In every larger town in Vienna is a taxi service.  
taxi © Rainer Sturm/
Taxis are equipped with officially calibrated taximeters ( basic fee in Vienna is € 2,50 in day and € 2,60 at night ). Tariff can be counted by mileage or time. In Vienna isn't valid any surcharge for luggage.
On the way from the Vienna to airport it's necessary to order airport taxi - "Flughafentaxi" In price of fare is fee for return way empty taxi of   € 11,-.
Airport taxis are special taxis only for way, from and to airport. They wait right on the airport in Schwechatu. It's necessary order it beforehand. Price of fare is fixed without fee for luggage and return way of empty taxi.