Selfhosted

If you go old PC and use it for Jellyfin, you probably want hardware that can do accelerated video transcoding so you probably want to aim for 8th gen or newer Intel CPUs (with integrated graphics), because that gets you 10bit h265 transcoding, which I'd say is probably the bare minimum you should aim for these days.

Granted that's 5 or 6-year-old hardware, so it's hardly new, but it took me a bit to figure out why in the world the transcoding performance and quality sucked and what's supported where and at what gen of hardware is... hilariously unclear.

Get an laptop made in the last 5 years or so and put in a 2 tb ssd and you’re off to the races. Install pop os or Ubuntu Linux on it and use a low memory windows ux like LXQt or run it headless

If you are doing Jellyfin, see if you can score an old graphics card to help with transcoding. I use old 1050ti cards.

I mean, you've got the answers I normally give in your last paragraph. I personally like mini PCs, I usually look for something refub'd, as new a processor generation I can find, and that I can upgrade the RAM to 16 or 32 gigs. M2 is nice but not necessary, I broke my M2 slot out to a PCI-E riser to add a 10g card in the jankiest way possible. Also, if you're doing transcoding with Jellyfin you're probably not going to have too great a time with mini PCs if you want more that like 2 or 3 streams at a time unless you make sure to get a higher-end processor.

SBC's like Raspberry Pi's are ok, but tend to suck for fileserving tasks like Jellyfin. Their CPU's are poor IPC and will choke on transcoding video, and they're pretty I/O limited too. They'll work but they're not scalable if you're expecting more than one or two users. And straight up forget using the onboard SD cards for storage, they're slow and will commit suicide as fast as you can replace them.

Some SBC's with better I/O and CPU's exist, such as the Orange Pi 5 I just bought which supports a NVME M.2 2242 drive and has a CPU roughly 4x the overall performance of a RPI. However, they're also not cheap- a decent specced OPI5 with 8gb of memory will still run you $100. And they require the addition of aftermarket cooling to not thermal throttle constantly, which will take some tinkering. Given how bloody cheap flash memory has gotten though- you can get lower end 1TB M.2 drives for like $60- they're a half decent option for a very power efficient and compact little set-and-forget self host board that can hold a respectable amount of media.

Next best thing would be to shop around Facebook Marketplace or Craigslist and find a SFF office PC like an Optiplex 9020. Try to get a i5 CPU for 4 cores, and a minimum of 4gb of RAM although 8 would be ideal. They're small enough, although they will use significantly more power than a SBC (typical low-load idle for my 9020 is around 30W from the wall- under load it's 110-120)

Laptops are more power efficient than SFF's but you have to be careful that they have removable batteries. Li-ion cells can and will start to puff up when run fully charged at high temperatures, such in a closed laptop doing server duty.

Le Potato is pretty great, I have a few. Make sure to get a case if you go with it. Maybe do it for DNS and display and later a cheapo used computer for jellyfin if your appetite is whetted

I am running my home server on a Dell 3050 from shopgoodwill.com and it was ~$40 without hard drives. It has room for an m2 drive and SSD so I have Ubuntu/Docker on the m2 and all my data on an SSD.