Linux

If you don't need transcoding, then anything should be able to handle it. But, if you are planning to stream over the Internet to your phone on LTE, you'll "probably" want transcoding, or if you are streaming to set top boxes, they may not support the codecs you used, and will also require transcoding.

I personally am using Jellyfin, and find it to be great for TV shows, movies, and you tube (via tubearchivist + its jellyfin plugin). It's dead simple to setup, its metadata is perfect, and there are great frontends for it. Other than the big update from about 6 months ago, it has mostly been a set it and forget it.

Some people use jellyfin for music, but I find navidrome a much better option for music.

I run my media server on a fitlet2. It isn't super powerful, but has been a great little machine. It can transcode 1080p just fine, but would struggle for doing anything higher than that.

It hosts about 30 other things too, including my camera and NVR with frigate.

I’d look at retired business machine, preferably something small like Lenovo or Dell SFF office pc, with 8th gen i3 at minimum. 8th gen is where the integrated gpu shines for this purpose. Install plex or Jellyfin. And if possible, stick to internal drives instead of external; one fewer thing to draw extra power. You could even do a second drive internally for backup.

here’s someone who installed linux on one.. If you need WiFi make sure you understand how to add the Broadcom module into the kernel.

The 2014 minis are all dual core haswell CPUs so don’t bother with the hotter i7 versions. You can’t upgrade the ram so buy what you need.

If you’re in Europe often the hp elitedesk is a used pc of note. The elitedesk 800 g4 specifically may be a better option since the sff ones can already have bd drives built in, can take extensive internal storage upgrades (2x nvme, 2x 3.5, 1x 2.5) and will have a four core eighth generation intel processor 99% of the time which makes 4k within reach.

Kodi is the media system package used by a lot of linux systems. Libreelec is a linux distribution that focuses on running kodi.

If your stereo has hdmi you can just plug one into the other and hear movies and tv sound through the stereo, if not then you’ll will need to do some kind of input switching to listen to music using the 3.5mm jack and movies using sound over hdmi.

E: don’t worry about power efficiency. Even the 2014 Mac you’re looking at is able to turn stuff off at the processors clock tree and idles at a low enough draw to not worry about.

One thing you might consider is skipping buying the Blu-ray player and obtaining your movie rips alternatively. Only you know your appetite for risk, but so long as you’re only getting copies of the movies you own, I’d guess the risk is small. Besides, simply ripping your physical discs isn’t strictly legal everywhere, so that itself may have a small risk.

Put the money you save into a better machine.

My media server, which is just my server generally, is an old thinkpad I have from 2014. For media I use Jellyfin and I ensure the content is already in a format that will not require transcoding on any device I care to serve to (typically mp4 1080p hevc + aac).

If you look at the used computer market, there are endless options to attain what you are asking for. My only real advice is make sure the computer doesn’t draw much power and, if possible, doesn’t emit much or any fan noise. A laptop is a decent choice because the battery kind of serves as an uninterruptible power supply. I just cap my charge limit at 80% since I never unplug it.

Just sharing a little side project.

I wanted to write a side project for media streaming to see how things like Stremio work

Wrote a very minimal client in Go which took 5 weekends and I've so far been able to get it to look up something by tmdb code, grab it with prowlarr, Transcode when needed, present it as a link to work in browser

I've been slow with it but I'm pretty proud for both having no experience and not vibe coding (just good old-fashioned code theft off of Stack exchange sometimes)

Probably absolutely garbage but hey I learned a lot

Hardware

A mac mini is probably overkill for what you want to do. We are talking standard blu-ray after all, meaning your videos are going to be limited to 720p. Most hardware will have no problem dealing with that. The cheapest solution that's fit for purpose is a refurbished thin client. They aren't powerful or anything, but you don't need powerful. You need quiet (passively cooled) and low on energy consumption.

Thin clients can be had on eBay for less than 30 Franks.

Software

• Kodi: originally known as the XBox Media Center (XBMC), a TV friendly menu to pick the movie or TV show you want to watch
• LibreElec: A Linux distro, that preconfigures and auto starts Kodi, not the best choice if you plan to use anything besides Kodi
• Jellyfin: A media server. If you got multiple TVs you might want to look into this one. It essentially let's you operate your own Netflix, complete with a web frontend and apps for phones and TVs, integrates with Kodi

Libelec (kodi) is fine if only playing local media but its use for anything else except realdebrid is extremely lacking. On the plus side it will run great on an Rpi5 and if you go that route you can probably even use your TV remote because Libelec has excellent CEC support.

Jellyfin/Plex is something your TV also probably has an app for, so you wouldn't even need a media center, just a media server.

Plasma Bigscreen is making slow gains, but in a couple of years will probably be the definitive Linux media center PC.

Also a bit unconventional, but Bazzite can load directly into Steam's big picture mode. From there you could set shortcuts for Jellyfin or Plex HTPC.

I wouldn't use an old MacMini for much because they aren't actually power efficient, but any n100 for Ryzen5 minipic with Kodi on it would work just fine for you want. There are plenty of altern6to Kodi, but it's so simple, it's hard to pass up.