That's how I started, when I upgraded my PC my old PC became a dedicated Plex server running Linux, then the CPU gave up after 8 years (3 years as a 24/7 sever) then bought a PC to run unraid. Its a slippery slope, I started on 16tb of media 6 months ago, I'm now on 24tb...
I had to upgrade from that once it started struggling more and more with higher definition content. I ended up upgrading my desktop and using the old parts to build a server machine. The only things I had to buy was a PC case and some hard drives.
You can get a Mini PC with a modern laptop chip inside it to get the power savings and save some space too. Not only that, but you get the advantage of a potentially more modern chip too. I tried my new setup (Ryzen 5 5560U) with 4K HDR decoding last night and it worked without a hitch.
This thread came at the perfect time. I'm looking to set up my own Media server.
I love the suggestions already posted, does anyone have any more suggestions about which software and hardware to use for this sort of thing? I have an old Macbook 2013 running PopOS that I was thinking about using but I worry it'll have issues being powered up 24/7.
Or, and hear me out here, get an old dell i3, and a couple 6tb hdd to run unraid, with the arr's and plex in dockers. Then decide that's not enough storage, so you get some 8tb drives. Then decide you need some mote space, and you might as well upgrade the chip. Plus you need a GPU to transcode, and the Dell won't support that. So now you've got a fractal Define R5, Asus MOBO, Nvidia GPU, i5, 8 14tb hdd, 2 more 14 tb hdd's for parity, 2 120gb ssd's for cache, and noctua fans to keep the noise down. So what I'm saying is I might have a problem.
In use an i3 12100 with whatever cheep motherboard from a good brand and 16gb of ram (it would be fine with 8gb, but DDR4 ram is cheep so more the better) if you look at ZFS and a real raid, it gets expensive quick, I use Unraid which is ideal if you have SMR drives and/or different sized HDDs. You can get cheep LSI HBM cards off eBay in IT mode which is perfect to connect HDDs to (my mobo only has 4 sata ports)
That's how I run mine, though I think I may have a 10 or 11 series i3. It idles just under 30W, which isn't too bad, and - though I don't have lots of users - never breaks 40, even during 4k transcodes, thanks to quicksync.