My first homelab thing was a laptop with a broken monitor. It wasn't terribly hard to get Ubuntu server working on there, it had a gigabit ethernet port built in, and it had USB 3.0 so it wasn't too hard to get reasonably good hard drive speeds to use as a NAS.
You can buy old used laptops (especially with broken monitors) for basically nothing (or maybe literally nothing if you already have one, or you have a friend of family member who has one they're willing to donate). If your goal is just to use it for Plex, it will work fine, and the power draw on laptops (particularly when idle) isn't that much more than a NUC.
I use a proper rack mount server now largely because I thought they were neat, but I think for most people an old laptop is fine.
That's my setup. I decided to use old laptops instead of proper servers because power cuts are common in the region I live, especially when it rains. So laptops have built in UPS (their batteries) which can hold power for some minutes in the worst cases. It sounds like a poor man's home lab, but it works.
Honestly, I think that's probably smarter than what I do now. My personal laptop idles around 15-20W, tends to peak at about 80W. If I bought a dozen laptops, the total energy usage would be roughly the same as my server at idle, and I could use Docker Swarm or something to glue everything together, while also having a lot more power resiliency because of the batteries (like you mentioned).
I also think it's good to prevent ewaste. There's a lot of raw computing power that just ends up in landfills. It's almost certainly better for the environment to get as much use out of existing stuff as possible than it is to buy new stuff. I can't imagine it's good for the world for a bunch of old lithium batteries to lie dormant.
If I can find a good deal on a dozen old laptops, I might honestly put this plan into action.
You can buy old used laptops (especially with broken monitors) for basically nothing (or maybe literally nothing if you already have one, or you have a friend of family member who has one they're willing to donate). If your goal is just to use it for Plex, it will work fine, and the power draw on laptops (particularly when idle) isn't that much more than a NUC.
I use a proper rack mount server now largely because I thought they were neat, but I think for most people an old laptop is fine.