For those of us who may not have searched ground transportation before we arrived, I have a one word solution...CAT. City Airport Transportation is the simple way to go. They have lime green ticket kiosks all over the baggage area, also a desk to your right as you leave the baggage area. It couldn't be more simple. Their train into Vienna runs every 30 minutes at 6 and 36 past the hour. You needn't worry about getting on the wrong train, because they have painted their trains the same colors as the kiosks.
At this writing, there are 2 types of tickets. The 12 euro ticket is for the train only, but the 2nd option, costing 14 euro, includes an underground Uban ticket. Lines 3 & 4 are available at the end of your train ride, just outside the train station. Luckily for us, our hotel was just a block away from a U3 station, so no transfers were required.