Munich-Vienna-Prague-Munich

, I will need to get to Vienna from Munich Airport. (Is there a train that leaves from the airport, or will I need to find my way to Munich Hbf first?)

You will need to take S-Bahn to Munich Haupftbanoff to get train to Vienna.

You can use these sites to search route prices and/or buy tickets

train;
https://www.bahn.com/i/view/index.shtml

bus:
https://www.flixbus.com/

There are no long-distance rail services from Munich airport for this route, you will have to take the S-Bahn (light rail) to Munich Hbf. But you can buy a ticket all the way through from the airport to Vienna. There are a few times for end of April dates that still have deep discount tickets available for 29,90 EUR, other times already show higher fares of 39,90 EUR or 69,90 EUR. Full fare is about 104,90 EUR so it's worth buying today if you're ready.

If you don't yet know, bahn.de is the best place to look for all your routes, but you can only buy tickets through them for routes that touch Germany at some point, so your first and last legs. For Vienna to Prague, buy through oebb.com.

There is no reasonable train connection between Prague and Munich.
Going by bus is cheapest: https://czech-transport.com/index.php?id=2604
Cheapest flight is about $125: https://www.kayak.com/flights

You can indeed buy tickets for Vienna to Prague on oebb.com but I would also try cd.cz - they are usually cheaper.

RegioJet trains run from Vienna to Prague for 15 Euro. I’d go with that.

You can also check out Flixbus they are having good deals and always new lines connecting cities!

Thank you ALL for the great input!
I haven't booked a train ticket yet for Munich to Vienna, as I don't know how long it'll take to get through Customs and find my way to Munich Hbf. Looking at the DB/OBB websites, it seems that taking a RailJet train is the most direct with only 1 connection, but it's a steep € 105. As mentioned by Nelly, there are cheaper tickets, but it comes with more connections (and probably greater chances for me to miss my connections and/or get lost).

Tickets booked: RegioJet train from Vienna to Prague (€ 15) & DB bus from Prague to Munich (€ 25).

Thanks again!

Great! Enjoy your trip!

In the summer, direct Prague-Munich train service will resume to run about 7x/day, but for spring it's cancelled for track work.