The most cost effective way to get from Munich airport to Salzburg is with a Bayern Ticket. Cost is 27 EUR for one person (assuming you are traveling alone, as you say "I", not "we"). You must travel on regional trains only. Since Sept 15 is a Friday, you must travel after 9 am. That should not be a problem even if you arrive early Friday morning, for by the time you deplane, go through Schengen immigration, get your luggage and make your way to the airport train station, it is probably after 9 am. If by chance you arrive early, just remember not to board a train until after 9 am.
Taking either the S-1 to Munich Hbf, or the S-8 to Munich Ostbahnhof and transfer to the hourly regional train to Salzburg. Do not take the Railjet or Eurocity trains as the Bayern ticket is not valid with those trains.
If you did want to visit the Oktoberfest, you can do that from Salzburg also with he Bayern Ticket. It is valid anytime on weekends, so you can travel early on the 16th. 27 EUR is good all day on the regional trains so that will get you to Munich and return on the same day, and include Munich city transport. The Theresienwiese is not too for a walk from Munich Hbf, or you can take the U-Bahn one stop to the Oktoberfest grounds. As said, there is a big parade on opening day and they have a keg-tapping ceremony at noon. There are carnival rides and other activities at Oktoberfest. In fact, on opening day, it will be impossible to find a seat inside one of the tents. You might find a seat on one of the outdoor picnic benches.