The best thing you can do is taking the train.
Taking a car is really not the best choice because the A3 (FRA-NUE) is quite busy and there a several constructions. It can take between 90mins and 5 hours....
And the gas price is approx. 5USD per gallon!!

At FRA you have a very convenient connection between plane and train.
You will arrive at T1 concourse C. After picking up your luggage follow only the signs "Long Disance Trains". You won't have to leave the building because there is a path from T1 to the train station. You can purchase a ticket at the "Reisezentrum" next to the platforms or at http://reiseauskunft.bahn.de/bin/query.exe/en
(english version). After paying with your Credit Card you can print out your ticket.
For example the following trip is not too bad:

Frankfurt(M) Airport 25.05.04 dep 09:10 T4 ICE 721 Nuernberg ar 11:29
Nuernberg Hbf 25.05.04 dep 11:50 RE 20410 Coburg

You have to change at least 1 time in NUE

Have fun with the beautiful German Railway Service!!!