Trains.
Frankfurt to Heidelberg (spell it correctly) is a short trip, about ½ hour. I'd probably use a local ticket for this trip.
Heidelberg and Baden-Baden are both in the state (Land) of Baden-Württemberg. A Baden-Württemberg-Ticket (€20 Single, €28 for up to 5 P), an on/off day pass will cover your travel. Take the S-Bahn from Heidelberg to Mannheim, any regional train to Karlsruhe, and local transportation (reg. train or tram) to B-B.
Baden-Baden to Rothenburg for a beginner is probably best with a Baden-Württemberg-Ticket and a Bayern-Ticket (same prices). Take the S-Bahn to Heilbronn, then regional trains to Wurzburg, Steinach, and Rothenburg. You can get the Bayern-Ticket from a red Bahn automat at the Baden-Baden Bahnhof or for €2 more from the ticket counter.
Rothenburg to Munich requires a Bayern-Ticket, available from the local ticket automat in Rothenburg. Take the shuttle to Steinach, a regional train to Treuchtlingen, another regional train to Munich.