B1:
I second your recommendation regarding Potsdam and Weimar.

Do you have to stamp the ticket? It depends:
-When you take the S-Bahn or U-Bahn (Underground), you may have to stamp it.
-When you go with Bundesbahn, (mostly) not. Actually, sometimes I purchased the ticket on the train (from the Schaffner, Controller). I am not sure, if this is still possible today.