travelling by car from Baden Baden to Stauffen

There is a Steves-induced misconception afoot that Baden-Baden (spas, casinos), Freiburg (city, over 200,000 population), and Staufen (not very Black-Foresty but OK), have something to do with the Black Forest. In fact, they are all somewhat peripheral.

The Black Forest brings to mind small villages, farms, traditional ways, half-timbered houses, and great scenery... and perhaps some trees. If it's the Black Forest you wish to see, you may want to have a look at some different places. Gutach im Schwarzwald is a bit more central and relevant. See Gutach's tourism website: http://www.gutach-schwarzwald.de/startseite/20/en/home.html

Here are a few other Black Forest towns that you might investigate near Gutach and on your way to Füssen:
Gengenbach
Schiltach
Villingen
Haslach
Triberg

To answer your question, "which city is best to sleep over", all things equal, I would rather stay in a town of 7600 (Staufen) than a city of over 200,000 (Freiburg). Just my personal preference. Of course, it all depends on whether or not you can find suitable accommodations in Staufen (you can if you know where to look).

I've never been in Staufen, and I have only changed trains in Freiburg, but I did spend a day in Baden-Baden, and that was enough to convince me that I wouldn't bother to go there again. I prefer small towns in the northern Black Forest. I've spent over two weeks on three trips in Bad Herrenalb, three nights in Freudenstadt, and two nights each in Bad Wildbad and Alpirsbach, as well as a day's visit to Calw.

There are a number of train lines (like the Schwarzwaldbahn) connecting major places in the Black Forest as well as an extensive network of buses. No one needs a car in the Schwarzwald.

I agree w/ Lee that trains will work and a car isn't needed but either way, it's just an overnight stop... so... what's "best" for transportation might depend on your specific plans for that day (which remain unstated.) I suggested places that could be interesting to visit whether by car or by train. What's "best" for overnight?? I suppose that depends on what you plan to do on those days, or in the place you overnight. It might only be a matter of finding a room that suits you somewhere along the way.

Here are some maps with relief colors showing the locations of the towns we've suggested; they're train maps but you can drive to all these towns as well, naturally.

https://upload.wikimedia.org/wikipedia/commons/4/4d/Verlaufskarte_Schwarzwaldbahn_(Baden).png

This map shows the train line between Freudenstadt and Hausach: https://de.wikipedia.org/wiki/Kinzigtalbahn_(Schwarzwald)#/media/File:Verlaufskarte_Kinzigtalbahn.png

Note that train users will now find a station at Gutach - not shown on the maps, but a recent addition.

Shouldn't be a problem in 10 months, but we were in the Black Forest in late October of this year & tried to drive from Titisee to Staufen for the night, but the road was closed due to construction & neither our GPS nor the locals could give us an alternate route to Staufen, so we had to spend the night in Titisee.
Driving from Baden Baden to Titisee reminded us of driving thru the Smokey Mountain National Park. Maybe the route we took had a few more hills, but if you are pushed for time, you may want to take Rick's "short drive" - we wished we had.

We loved Staufen because it was small and quaint, and there was a bit of a town to walk in at night.

We decided not to travel through Freiburg, and stopped in Triberg and Tubingen instead. We loved Tubingen !