MediaFormat

Media formats

Sound

The sound should be provided as mp3 or wav files. These formats do not seem to cause any issues and can be played by the sound player.
Video
-
The video format is another story. It seems that JavaFX media player is a bit picky with respect to the supported media formats.
The format Codec: H264 - MPEG-4 AVC (part 10) (avc1) at least seems to work. You can convert the MP4 file that is created from the animation render in blender with this comand line on Linux:
ffmpeg -i <input.mp4> -c:v libx264 -c:a mp3 <output.mp4>