Q: Which Recording settings on the application will give the best, highest quality audio?

A: The default settings 16000 sample rate and 64 bit rate is absolutely fine for most cases.
Theoretically 44100 gives better quality, but Skype uses 16000 inside when encoding audio. So basically this can only slightly improve audio from mic.
128 bit rate give the best quality, but it is almost indistinguishable difference for human ear when speech is encoded.
I would recommend to stay with defaults unless you have some specific requirements for mp3 encoding.

Mode doesn't change quality but the way audio is stored in file
stereo - you voice from left channel and the person you are talking with from the right channel. Good for transcribing as some times you may have two sides talking simultaneously. The volume can be different in different channels and you can balance it after.
mono - both voices in one channel. If you have only one speaker you may need this setting.