Any of them will work fine. I use ASIO just because in general with ASIO there is less interference from the OS. In general WASAPI is probably the most reliable (least twitchy to setup, best supported by the OS.) But the Thesycon drivers seem to work well with any of them.
Some claim to hear sonic differences between them, if you do just pick the one you want.
I’m having a problem with certain DSD tracks in JRiver (20.0.41).
I get the error message:
Something went wrong with playback. Details:
Playback could not be started on the output ASIO using the format DOP 2.8MHz 6ch. The ASIO device “PS Audio USB driver” does not support 6 channels. (card supports 2ch max).
I have the DSP settings set at 2 channels (stereo) and mixing: JRSS mixing (recommended).