Just remember that the track is practically a public road which any doofus can drive for a per lap fee What I would do is drive fairly conservative as there is no point by, run groups etc.
For a great road to drive try the Schwarzwaldhochstrasse. It runs on the ridge of the Black Forest mountain range and much of it is going south/north in the direction you need to go anyway:
Schwarzwaldhochstraße - mehr Schwarzwald geht nicht.
You can work your way up the Black forest from a more southern point as well, as it starts pretty close to the Swiss border. Any road in the forest will be fun.
Have fun and be safe!
G