Munich Airport to Munich Train station to Salzburg

Take the S8 to the Munich East (München Ostbahnhof) station and transfere there to a regional train called "Meridian" to Salzburg (runs hourly). No need to go to the main station. The cheapest way to do that is with a Bayern Ticket (valid on workdays after 9am, weekend all day) for €25/1 or €31/2. It covers both the S-bahn and the Meridian to Salzburg. No reservation needed or possible. Look up connections at www.bahn.com (to filter out pricy high speed trains activate the local trains only option). Buy your ticket from a vending machine at the airport or with a €2 service surcharge at the DB ticket counter. You will find both in the airport center (signposted from the gates by a "Z" = "Zentralbereich").

I hope you have been looking at the Deutsche Bahn website sla019 mentioned, and not Rail Europe, which would be no help at all. When I look it up for your travel date, time and enter 2 adults traveling from "Munich Airport T" to Salzburg Hbf", I get all the connections. Looking at the column under "Savings fares", all the ones with a price of 31 EUR are with the Bayern Ticket. Your Bayern Ticket is valid on any regional train (Meridian is a regional train), S-bahn, and local transit in Bavaria, including to Salzburg, Austria, for the rest of the day.
https://www.bahn.com/en/view/offers/regional/regional-day-tickets.shtml?dbkanal_007=L04_S02_D002_KIN0060_REGIO-INDEX-LAENDERTICKETS_LZ01

Note that all the connections list departing from the airport at 24 past the hour, but they are just listing the tightest connections with the S-8 that goes from the airport and stops at Munich Ost before continuing on to Munich Hbf. It goes every 20 minutes, The S-1 also goes every 20 minutes and goes to Munich Ost after it stops at Munich Hbf, such that every 10 minutes there is a train into Munich. So you are under no obligation to take any particular train with your Bayern Ticket. You could even go to Munich Hbf, store your bags in a station locker, and look around Munich, then catch the next hourly Meridian train to Salzburg from the Hbf (main train station). They leave from Hbf at 5 before the hour and stop at Munich Ost at 3 past the hour.

Thank you so much for the clear and helpful information, I can just relax now. You are great resources.
Rita

The S-8 leaves the airport station from Gleis (track) 2 and goes around to the east end of Munich to Ostbahnhof, then through the S-Bahn tunnel to the Hauptbahnhof and on to the end of the line SW of town. The train will show a destination of Herrsching or Weßling.

The S1 leaves the airport station from Gleis 1 and goes around to the west end of Munich and through the S-Bahn tunnel under Munich, ending at Munich Ost. It will show a destination of Ostbahnhof.

Don't be confused. S1 shows the destination of Ostbahnhof because that's where it terminates, but that is not the train you want to take to Ost. The S8 gets to Ost sooner, but it shows another destination because that is where it ends up. Take the S8.

Thanks everyone, I'm feeling confident with this information