Thanks for all the information.

My other concern, besides booking these journeys, is that I have read the Budapest train stations are almost impossible to get out of without being bothered by unscrupulous people trying to take you for a long and costly ride to your hotel. They say the hassle is almost unbearable. Any ideas on how to avoid these people? Is this also true of Prague? In the past, we have done a lot of train travel in Spain, Italy, France, etc. and found it a most civil way to travel. Not sure about eastern European countries.