We are planning this trip for October. I have considered travelling between these places via plane, train and private car service.
My inclination is to go with the train. What I am mostly curious about is reliability of service. Anybody have an opinion on this?
I'd do all trains. I found them reliable in the 3 countries you are visiting; but if you have money for a private car service that will take you to the front door of your lodging go for it.
I've done all of this other than the leg from Berlin via train and it is fine. Although I find the Czech train system less reliable than their neighbor's systems.
We are going in April and will do Vienna-Cesky Krumlov (overnight)- Prague with CK Shuttle, then train from Prague to Berlin with a 26 stopover in Dresden. So a mix of transport for us. These are the only 2 one night stops on a 26 day trip. I can let you know how it goes!
Last year I took the train from Berlin to Prague with a stop in Dresden. You can book the train that way and save money. The train was very good. If heading south sit on the the right side the scenery is beautiful. Enjoy