train from Prague to Vienna to Budapest

First, have you bought your airplane tickets? If not, book open jaw (multi-city), starting in Budapest and ending in Prague, or vice versa. Be sure to check the price for each option; sometimes, for no clear reason, it's much cheaper to do it in one direction vs. the other. Then you research train options on Bahn, http://reiseauskunft.bahn.de/bin/query.exe/en. It's the easiest website to find schedules, connections, etc. However, you can't use it to get prices or to make bookings for your routes, as they are completely outside of Germany. I'm not sure for your routes it there is a discount for advance purchase, or if the routes sell out. If one or both of these conditions apply, you want to book in advance; if not, you can wait until you get there. If you want to book in advance, you book tickets on the website of national rail for the country of origin of the train. So, for Budapest to Vienna, it's MAV, http://www.mav.hu/english/index.php. For Vienna to Budapest or Vienna to Prague, it's OEBB, http://www.oebb.at/en/. And for Prague to Vienna, it's CB, http://www.cd.cz/en/. continued..

continued.. Most people fine second class totally acceptable, but some do prefer first class, which usually has roomier seats and can be less crowded. Your choice. The Man In Seat 61 has lots of pictures of train compartments, so you can see if you want to pay extra for first class: http://www.seat61.com/. Choose your country on the left, then scroll way down, past the directions on how to get from London to the country, to see his pictures of train interiors. Whatever you do, don't use Rail Europe for either research or purchase. They only show trains that they do booking for (and so do not show all trains), and they have a markup over the national rail sites.