Chiemsee and Berchtesgaden are southeast of Munich.
Pick up the car at the Munich airport where you will find the best car selection.. Also, you won't have any problem with getting transport to an "off site" car rental location where they may claim "Ich nicht sprechen English". Be sure to inspect the car for prior damage and have the car rental company document any prior damage on the car rental papers. Follow this same inspection/documentation procedure when you return the car.
Some folks pick a spot close to the airport to spend the first day overcoming jet lag. Your decision..
Pick up a good map of Bavaria (Southern Germany) so you can get to your destinations without getting lost. You can use the autobahns to get from the Flughafen (AKA airport)) onto A8 toward Salzburg without entering the local Munich traffic.. Study the map as there are several chances to make a mistake and get on A8 and wind up in traffic on the north side of Munich. Take A92 from the airport toward Munich then A99 East to A8 in the direction Salzburg . I usually use Google maps and take hard copies ..
Have a great trip!!!