Thin clients are the best for this. You can take your pick on an abundant of options on eBay.

Jellyfin isn't that power hungry, and it would run on a rPi if you set it up right. You're only problems are when it decides to transcoder file and you can get around that by using Kodi with the jellyfin add-on. (And choosing the native paths option. Kodi grabs all the data via, SMB, NFS, etc)

This way you can use Jellyfin as a media enrichment solution, not worry about the CPU or GPU encoding and just worry about watching everything.

I'm using a hp thin client, I got refurbished for 30 bucks of of eBay. Basically any thin client should be more than enough and they don't draw much power. The question is how many streams are you looking to facilitate simultaneously and at what resolution. Even a raspberry pi should be enough if you are only looking to stream one video at 1080p but it will struggle at two (and if you don't enable any hardware transcoding, you don't stand any chance). If you need more than that, you'll need something beefier

If your clients don’t need transcoding then a Raspberry Pi 3 or higher is enough. That’s all I use and it is rock-solid with 3 simultaneous streams (possibly more but that’s all I’ve ever had a need for).

If your clients do need transcoding, personally I would recommend looking for a different client or using Tdarr to convert your media to a standard format that works without transcoding.

First off, if your clients can play the files natively, then anything capable of running Jellyfin will work. You only need specific hardware if you're going to transcode streams.

If you need transcoding, especially if you're going Intel, anything 8th Gen or newer will work.

As for your Linux distro, use whatever you're most comfortable with. Ububtu LTS or an EL-clone are both popular choices.

I used a fujitsu q9000 mini pc, a superold thing running first gen i3m chip. It was also undervolted but performed fine for 1080p streams. 8 gb ram 2tb

Recently I upgraded to a Nuc i3-8th gen, 16gb ram and a 4tb drive. It can handle 4k and is much faster at transcoding.

The NUC doesnt consume much and works pretty well. Its also a more quite and lived in a big ventilated closet.

I used an old Thin Client (HP t630) for exactly this. I didn't used transcoding because all of it was used locally So it was fine.

Now i'm using a Lenovo Tiny with an Intel CPUs (i5 6500t) and some transcoding because i'm using it remote sometimes.

Thanks for all the recommendations. I went with this:

https://www.bee-link.net/products/t4-pro

OS was Ubuntu 22.04 LTS. It was surprising how easy it was to set up Jellyfin. I thought it would be a lot harder but it took very little effort.

I got an old laptop from my family for free and I turned it into my jellyfin server (among other home server-like duties). Power consumption is very low (7W idle, up to 28W when playing movies measured at the wall).