In 2018 - AirPlay and AirPlay 2 are the premier ways to play Apple Music. Most people will want to just connect their speakers to a computer or device and use Siri / AirPlay to queue up music.
If we go in a time machine back to 2015 - the situation was a little less clear, but using iPhone and Apple TV was still the best way to stream music over WiFi from many controllers.
(much of what follows is wrong and/or outdated, but were possible solutions at a past point in time)
Your iPhone is a first tier player in Apple Music. It would be better to just play the music on your phone rather than monkey with "remote". Send the music over the network to the PC rather than sending the remote commands over the network to the PC.
Remote options are:
- Wait for Apple's remote to get updated for the hot newness
- Get a VNC/RDC remote and control the PC (janky - but does 100% what the PC can do without needing anything else on the PC end) screen directly.
- Third party remotes like Rowmote Pro (I say like since I have a handful of iPhone to Mac remotes - just can't recommend specific PC ones)
The iPhone can AirPlay to a PC quite easily with software on the PC such as AirFoil for Windows and you're set with Apple's full fledged iOS music controls but taking advantage of the PC to speaker connection you have already set up.
Depending on how the PC outputs to speakers, you could also add hardware ($5 to $65) to get the sound from either the PC or the iOS devices to the speakers. You don't need to do that as there are several workable software solutions.