I'm from the German Southwest and now travel this route as a tourist. I'd definitely recommend Ams to Colgone (overnight stay there). Then "slow" train to Mainz (see castles from train scenic route along the Rhine, this route is not used by high speed trains) overnight in HD. Then on to MUC for a few days with day trips to Lake Starnberg and Garmisch via train. Then to Prague. Do NOT rent a car -- save the money. Everything is easily reachable by train. Buy your tickets in advance from the US on the internet if you can figure out and stick to a schedule. Or buy a German Railpass for a week. Enjoy!