What is the best way to get from Salzburg to Munich on a Sunday afternoon with luggage?
Trains run directly between stations that are fairly centrally located. How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it. The slightly slower trains are covered by a group/all-day rate called the Bayern Ticket, but not valid on RailJet departures.
Are you ending in Munich, the city, or at the airport?
I am going to the airport or a hotel close by.
If you are going to the airport, the fastest route is to get off the train at Munich Ostbahnhof (east train station) and transfer to an S-Bahn (S8) from there to the airport. If you are using a Bayern-Ticket and a regional train from Salzburg to Munich, it will stop at Ostbahnhof. Some of the express trains, on which you can't use with a Bayern-Ticket, don't stop at Ostbahnhof. The Bayern-Ticket will cover the S-Bahn to the airport as well as the regional train to Ostbahnhof.
If you use one of the express trains with a Sparpreis fare, make sure you ticket it all the way to the airport. It shouldn't cost any more, and then you won't have to pay extra for the S-Bahn.