Check eBay for used business micro/mini/tiny PCs. They’re pretty cheap, and low power consumption. They’re mostly Intel processors, so that’s what you make of it. If I were you I’d look for i3 processors 9th gen and up, i5 and i7 8th Gen and up for transcoding. They can hardware transcode pretty much anything but AV1, vp9, and hevc 12bit but the processors are powerful enough that they can transcode those to x265/264 to a device or two using the CPU without issues.
If you don’t plan on transcoding, I’ve had no issues with a 5th Gen i5 NUC doing server things, but I do offload any processor heavy things to my 7060 micro (8th Gen i7) machine if I want it done quickly.
If you don’t need a laptop, I’ve been having a blast with using mini/micro/tiny business PCs off of eBay. I’ve had zero issues installing Debian on them, and they’re designed to be easy to maintain by IT departments, so Wi-Fi, storage, RAM, and even CPUs are all replaceable. They are mobile CPUs, so if you need the heavy lifting of desktop CPUs, you’d probably need to go with a larger form factor.