OP: The safe answer is "what sounds best to you." That said, I prefer the method that bypasses the Windows Mixer, which can add its own unwanted interpretation to what you are listening to, and just adds another step in the audio pathway. Wasapi Exclusive and ASIO bypass the mixer, although ASIO requires that you have installed ASIO drivers that work with your audio device, while Wasapi is built-in to Windows. DirectSound uses the Windows Mixer, so you have to see-saw those settings with any of your own set in MusicBee (EQ, etc.). Wasapi Shared, as opposed to Exclusive, takes a different route than DirectSound, but still ends up at the Windows Mixer ("Abandon all hope, ye who enter here..").
Wasapi Exclusive requires that you allow your device exclusive mode rights/priority to use it, following the steps shown in your images posted in another topic on this thread. Audio is then passed directly to the device drivers, which in my opinion "is to be preferred."