Solution for logging into PC with macbook, using PC speakers to play music
In my experience, the performance and quality of Microsoft's Remote Desktop (free) is the best in the industry.  This isn't a personal preference but rather a trial and error using many other remote desktop apps.

In short... 

Using Microsoft Remote Desktop 10 or higher, there should be a new option to play music on the remote machine.  Once toggled, I believe you'll get what you're looking for.. This is accessible through the + icon (new connection) or the ✏️ icon (existing connection).




As an aside, there are some nuances to using RDP, some of which are shortcuts.  I would love the option to disable ⌘ + w, ⌘ + q as I tend to hit them on accident intending Ctrl + w, etc... but it'll only close the RDP session, not the stuff that's running on the remote machine.


The long...

Disclaimer: The solutions below may look subjective, but they're objectively evaluated for the requirement of 1. Free or not free.  2. Secure.  3. Play sounds on the remote computer.


VNC: (free and commercial) Comes in many variants (macOS built-in, TightVNC, UltraVNC, etc). Offers secure and insecure options.
Performance is the worst I've used but is viable on a very fast network.
Splashtop: Secure.  Cloud-based so you can get to it anywhere.  Performance is better than VNC.  Requests are routed through the cloud, so can be slower than other solutions on a LAN.  Linux support is still experimental
GoToMeeting, WebEx, AnyDesk, etc: Online meeting apps are great (performance, options, audio), but often contain tools designed for group voice conversations (dedicated phone number, etc), making remote access a toggleable feature, not ideal hoops to jump through each for a dedicated remote desktop.
TeamViewer (free and commercial): Secure.  Great quality, speed.  Universal solution on Linux, Windows, macOS.  Cloud-based so may perform worse than LAN-driven solutions like RDP and VNC, however in my experience out-performs VNC.
Microsoft RDP (free): Secure.  Performs best when connecting to a Windows machine.  Historically LAN-driven, but Azure's rise in success makes it more attractive over WAN too (popular choice for Windows Server).  Performance, speed and quality are the best if a Windows machine is what's being connected to.


RDP even has support for streaming content and some compositing, which is very nice for video playback as well as for a curated Windows 7+ compositioned desktop experience (thumbnailing, transparency, etc).



For your needs I believe RDP is the way to go, especially since they've offered the option to keep audio routed through the Windows machine, which wasn't available back in Remote Desktop 8.