In the past I have used a 2014 Mac Mini, usually running headless, to run Roon Core and other music-related processes (including HQ Player, BAACH4Mac, and the HD Tracks downloader). I currently have Roon Core running on a dedicated music server (the sonicTransporter i9).
I have tried running Roon Core both from a separate room (with a WiFi backhaul) and co-located in the same cabinet with all my other HiFi gear. Either way makes little or no difference to sound quality, but I prefer to avoid the WiFi backhaul. If I had ethernet cable (or optical fiber) lines throughout my house, I'd probably put my server in a separate room, just to make my HiFi cabinet a little less crowded. However, I never notice the sound of the Mac Mini's fan even if it is within 10 ft of my listening position, and especially not with music playing.
Any concerns about computer system "noise" are overblown, IMO. However, processes such as Time Machine may hog computing resources and interfere with music playback, so you may want to shut them off if or when you're using the Mini for that purpose. If you run Roon Core on the Mini, it's easy to control it from an iOS device. You also can use Screen Sharing to control a headless Mini from another MacOS device.
Using the sonicTransporter vs the Mini for Roon Core has little or no impact on sound quality, as far as I can tell. Nor does the choice of ethernet vs. USB, per se. Currently, I run both Roon Core and HQ Player on the sonicTransporter, mainly because it has a faster processor than my aging Mini. I also prefer a USB connection to ethernet, because I can only use HQ Player with USB. This pathway allows higher upsampling rates (up to DSD 512) than I can get with Roon via an ethernet connection.
If I were starting over from scratch and buying all new equipment, I'd seriously consider a new M2 Mac Mini rather than a dedicated music server plus a Mini. In any case, I wouldn't want to do without the Mini because it is useful for so many music-related tasks. Also, the Mini tends to be much less expensive than a dedicated server. Controlling it remotely is pretty easy. For a simple setup, I suppose you could just connect a Mini via USB to your HiFi rig then play Apple Music using the iTunes Remote app from one or more other devices (though I've never tried exactly this setup myself). Personally, I like Roon, but you have other options such as Audirvana. Tidal and Qobuz subscription services work beautifully with Roon. Apple Music does not integrate directly with Roon. Roon can index and play music from stored files in your iTunes Library, but cannot directly access Apple Music servers for real time playback.