I prefer JRiver Media Center over other players. Not necessarily because it sounds better than other players - if a player is decoding properly and outputting WASAPI exclusive, it should be bit-perfect - but because it has a much larger feature set than anything else out there, and is very powerful.
Unfortunately, with all this power, it can be intimidating to use and get it set up to act the way you want it to.
The more I use it, the more I am finding that it will almost certainly be able to do what you want, but you might have to check the Wiki or ask on the forums before you figure out how to do that.
As a Music Server, I don't think anything else comes close. It's
extremely powerful in that regard.
The other thing that's nice is that JRiver is not just a top-tier audio player - you have all of its audio features available when playing back video too, so it's the best video player out there as well as being the best music player.
What is the difference between an ASIO and WASAPI plugin? Is there a benefit of using one over another?
If your hardware has a native ASIO driver (i.e. the manufacturer's site has one for download) then ASIO generally has the most direct path into the audio hardware.
ASIO4All and other "ASIO" drivers are typically just wrappers for Kernel Streaming, and are not a good option. WASAPI is generally the best option if your hardware doesn't have a native ASIO driver.
There are a few types of WASAPI - Exclusive or Shared, and Event Style.
WASAPI Exclusive Mode allows the player to take control of the sound hardware and handle things like channel switching, sample rate switching etc.
Most hardware allows access that is on-par with ASIO when using WASAPI Exclusive Mode. Some hardware, such as the ASUS sound cards, need an ASIO driver for this level of control. WASAPI Exclusive Mode does not allow other software to send audio to the sound card, so you won't hear system sounds while music is playing.
If you do not use Exclusive Mode, the player won't be able to change sample rates on the card, and it has to be set to output the same settings as you have in the Sound Control Panel.
While playing music, you will also be able to hear other sounds playing at the same time - system sounds, videos playing in your web browser and so on.
Event Style WASAPI allows the device to pull the audio data as required, rather than the system pushing the data to the card. Generally I find this works a bit better overall, but it's not going to affect audio quality.