Any suggestions as to the easiest route?
Wien(Vienna)-Nuernberg-Ansbach-Steinach-Rothenburg ob der Tauber is your fastest route (a little over six hours). You can make one less connection, but your total travel time will be longer. See the timetables at www.bahn.de. After you get summary timetables for Wien-Rothenburg ob der Tauber, click on the arrow to the left of each departure time to see the connecting points.
If you book well in advance (up to 92 days allowed) on the DB site, you can get a Europa-Spezial Oesterreich fare as low as €39.