There is an Avis Station in Terminal 2, the cars are in the basement of the terminal. You can be in your rental car in 10-20 min after your plane docks and you have status with the rental company. Another 5-10 min to get out of the parking structure and onto the Autobahn.
Two providers you should compare is www.sixt.de and www.europcar.de.
For driving distances check www.mapquest.de. There are several Rothenburgs, so make sure you get to the right one. zip-code (PLZ = Postleitzahl) helps.
Calculate 100 - 120 km per hour average on the Autobahn and 60 - 80 on regular roads.