Is RailEurope a good website for getting train tickets?

No, it will cost more but it may be easier. Go to www.seat61.com for help with booking train tickets and reserving seats.

Rail Europe isn't able to match the advance-purchase discounts offered by Austrian rail, which operates your second and third train legs, and also used to have a better connection to all the German rates then it seems to have now. The German rail site sells the advance discounts for the two trips touching Munich and that's easy to use if you're ready to lock in dates and times. Since the Austrian web site can less user-friendly and doesn't like some American credit cards, see Seat 61's advice on how to get the cheaper tickets departing Prague.

Used to be, but do not know now, that RailEurope also sold only the premium trains, leaving out cheaper intercity trains and other tickets that would be available on the Country sites.

No and no.

RailEurope is a travel agency, they mark up the train fares and they operate no trains.

Munich to Prague - 15 Euros; use this link for instructions - https://www.seat61.com/trains-and-routes/munich-to-prague-by-train.htm

Prague to Vienna - 14 Euros; use this link for instructions - https://www.seat61.com/trains-and-routes/prague-to-vienna-by-train.htm

Vienna to Munich - 29.90 Euros; use this link for instructions - https://www.seat61.com/international-trains/trains-from-Vienna.htm#Vienna-Munich

The fares above are for advance online purchase tickets for a train at a specific time. You can also buy the tickets at the station, but the fares with be 3-4 times the price mentioned above, but have full flexibility. These tickets bought at the station will still be cheaper than RailEurope. That said, everyone buys their tickets online in advance for a specific train. No one with any travel sense buys tickets at the station.

Munich-->Prague

Never buy tickets for that connection from RailEurope (most expensive) or from DB (trains are not operated bythe DB but by an joint venture of Czech Rail and the Bavarian Laenderbahn). The best prices has the E-Shop of Czech Rail: the regular ticket Munich - Praha is over €70, prices at the Czech web site start from €15 (you will be locked into a specific train). If cheap tickets ("Europe first") tickets are sould out you can always resort to a "Prag Spezial" - ticket (€39, valid on any train). There are also buses, departing from the ZOB at Munich Hackerbrücke (one S-Bahn station from the train station). For an overview look up busliniensuche.de.

Just avoid RailEurope in general and buy your tickets from either the national rail companies of the countries you’re visiting or from a reputable 3rd party like trainline.eu

Glad you had the foresight to come here and ask first...so many people just get RailEurope and Eurail Passes in their head and blindly make purchases with very little info.

Be careful about Trainline. When they started, their prices were matching German Rail's, but now it seem like their prices are about 8% higher. Some of this might be a surcharge for the interchange rate taken by American credit cards, but it can't all be. Their prices are about 5% higher than the Bahn, plus they are adding a service charge of about 3%.

From the Netherlands Trainline gives exactly the same prices as the Bahn. So it will probably have something to do with the banking part of the process.