Would you recommend that I buy a 3 country rail pass or buy each trip ticket separately for the above trip. I also want to take a day trip from Prague to Dresden in Germany. Any idea of costs for all the above?
You can figure that out for yourself by using the national train sites. For example -- in Germany, use bahn.de. I would doubt if a pass would save money given limited amount of train travel.
For the Budapest to Vienna leg, you may find it is less expensive to take the Orangeways Bus. We waited until we got to Budapest to purchase tickets to Vienna (March 2010) and found the train tickets would cost 10,000 HUF/person (about $50) while the bus cost 2110 HUF/person (about $11). The bus was fantastic.