music transfer

It's likely that a home stereo component will not have a USB output.

Typically you'd have a stereo analog output (pair of RCA jacks), and maybe an optical digital output. If the player was also a DVD or Blu-Ray player, it would usually have HDMI in addition to, or instead of, these.

You could buy a USB sound card and use it to import the analog stereo output of the home stereo player, but that would introduce additional D-to-A and A-to-D conversions that would not have to take place if you imported your music from an external USB optical drive designed for a computer. And you wouldn't save much money.

If the player has an optical digital output, and your Mini's headphone jack is one of those that is able to double as a Mini TosLink port (check if Apple's technical specifications for your Mac mention optical digital audio input), you might be able to connect a suitable optical digital audio cable between your player and your Mac.

A HDMI output wouldn't help you at all. The Mac Mini's HDMI port is also for output – not for input.

In either of the first two scenarios, you would need software on the Mac to record the incoming audio and to help you manually chop up recordings into individual songs. An external USB optical drive seems like a better solution.

If the Mac mini can see the player on a USB connection, then you maybe able to Import CDs into the Music App.

If not, then you need an external USB DVD/CD drive to Import your CDs.

Personally I prefer using my tray loading LG DVD/CD drive over using an Apple USB SuperDrive.