There are three things to consider:
- Storage of the music.
The music files have to be available to the Pi. This means setting up up a share on the Pc so the Pi can access the files and having them in the correct format.
- Connection to the stereo.
The Pi has very basic audio capabilities and I would look to one of the many many HATs that are available others are available). The majority of these use I2C to link to the Pi and provide a digital to analogue converter. You will need to find a HAT that outputs signals that are compatible with your stereo. Note Aux ports can be input (from an auxiliary device) or output (to an auxiliary amp and speaker set).
- Something to provide control
This piece of software has to reside on the Pi, link to the music, link to the HAT on the Pi and take control. Sounds a lot but it's a common need and a search for Pi music players will give you lots and lots. My personal choice is Volumio - I am not affiliated to them but a happy user but this takes over the Pi completely as it can:
- Link to remote sources of music
- Index the music (inc album art) without being concerned on the music format as long as the music meta data is present in the file
- Let you control it from a web browser on your PC or an app running on Android or IOS devices. I think the Android app handles multi-room sync'd output where as my iOS version does not. The apps are chargeable - this is one way they fund the development BUT web browsing on my iPhone is fine as the page is reactive to device size and orientation.
- Output via the HAT or to Bluetooth devices (inc cheap portable Bluetooth headphones and speakers)
Lots of alternatives are available (see here for some examples) but I would also think about:
- Is you output (i.e. amp and speakers) capable of decent music playback?
- Does your collection have the correct data esp album links?
- Would you be better just to get a small portable set-up that takes a SD card?
You can find a few videos about this by John Darko on YouTube He is an audio nut so some solutions are the cost of a small house but there are a few Pi based ones as well.