First of all, congratulations!

Taking the train for this area is the smart solution. Well done. You might be able to get a Eurail pass to lower your cost but others will know more about that. How much time do you have? It is difficult to propose a full tour with routes, of course. But the good thing is that wherever you want to go, the train will take you there; it's a very dense network. Another question is how far into each country you want to go. What I mean is that Austria extends really far east, actually Vienna is pretty far east, and Switzerland extends quite far into the west towards France and the south towards Italy. Germany on the other hand goes all the way up to Denmark.

Given that Frankfurt is your base, it would make sense to confine this trip to the southwestern part and do the northeastern part another time. Unfortunately, this means that you will have to exclude Vienna on this trip, as well as Hamburg, Berlin, Dresden. BUT you can still see Salzburg, Bregenz, Innsbruck in Austria. In Germany, I would suggest doing Heidelberg, Munich, Konstanz and Lindau. All of these have gorgeous architecture and landscape and beer, of course. In Switzerland, you could do Basel and Zurich without a problem.

Now if you wanted just the top spots in each country, my personal selection would be not very original and I would tend to favor big cities (which can be just as romantic).

Germany: Hamburg, Berlin, Munich
Austria: Vienna, Salzburg, Bregenz (Lake of Constance area, absolutely gorgeous in early September)
Switzerland: Basel, Lugano (drive through Alps, maybe go see the Montblanc)

You could still do this schedule but it would take you 20 days not to be stressful and you'd rack up some serious train hours.

Grab a map and check out what is where. This way you can literally map out a circuit that makes sense.

Till