I did similar trip last summer. On the map it seems be logical but actually the connection isnt somehow excellent. To safe money you have to buy international train/bus tickets in advance on-line otherwise will be the aircraft much cheaper. I took train "Frecciaargento" from Firenze to Verona (2 hours 30 eur) http://www.trenitalia.com/, from Verona to Innsbruck "EuroCity DB-OBB" (4 hours 40 eur) https://ticketing.oebb.at/inet/pub/en/ticket, from Innsbruck there are many trains to Salzburg, they pass through Germany but the price is like for domestic train, anyway its cheaper to buy them on-line (2 hours 15 eur).
From Salzburg you have to take domestic train to Linz/Donau (1 hour 25 eur), from Linz you have to take "rychlik" R train to Ceske Budejovice (2 hours 25 eur). From Ceske Budejovice you can take train to Cesky Krumlov (1 hour 2 eur). From Cesky Krumlov to prague I would recommend you to take a bus …studentagency.cz/Booking/… (3 hours 7 eur)
Thank you so much Milanek. Jim H
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