Good to see fellow countrymen here! For cheap but decent hotels, and especially in Germany, I would recommend Etap.
They are all over the place, have WC, shower, TV, clean beds and that is about it. Some are even unmanned at times, you open the front door with your creditcard and check in yourself. This was a sign in one of the hotels we stayed in...
It translates approximtely to "Here was originally the mini-bar, but we saved you some space - a service by the Etap Hotel."
Good luck on your journey, I'm looking forward to the rest. Interesting though that you don't consider our country being part of Europe?