Go to the tourist information center at the airport if you want to buy a multi-day-ticket for Vienna. You will need an additional 1 zone ticket extra to go to Vienna. If you only need a ticket to Vienna, you can buy a 2 zone ticket at a ticket machine.

Then use S-Bahn S7 to "Wien Mitte/Landstraße". Don't use CAT, it costs extra. And "Wolfsthal" would be the wrong direction. Current departures from Vienna International Airport: