Travel questions

Im going to be taking a trip to Europe sometime towards the end of summer, possible fall. I would like to be there from 10-14 days.

Prague -> Vienna -> Istanbul -> Athens

That is the intinerary I would like to maintain. I understand it is cheaper to fly out of/into major airports, so I would probably leave from NYC and fly into Prague, and leave from there as well. Another option would be to fly into Dusseldorf, as that would be a direct flight, then take a train to the other destinations.

I am really curious to hear from people with experience travelling in Europe. Is rail cheap/decent?

Also, if anyone has any tips for booking such a trip, I would GREATLY appreciate it, as I am a complete travel noob…

I understand its going to be $$$, but I would like to keep it somewhat reasonable…