You will have to pay for the bus from the Airport to the station in Memmingen. It is not really big - a very small town.
Forget about walking, the airport is fare outside - it is an old military air base.
You won't need long time to check out. There are only some flights per day and the air plane stops directly 10 meters in front of the main building where you just walk in and get your backpack.
From the station you have several connections to Munich main station (München Hbf) - all train on this route are free to use with a rail pass - it doesn't matters which one. Several connections are available per day - you won't have to wait longer than 1 hour - travel time around 2 hours:
The Wombats City Hostel is just some meters away (2 minutes) from the main station in Munich - you can walk: rail.cc/en/munich/wombats-city-hostel/l337