I was able to score this sound-proofed server cabinet for peanuts, some business was selling it off.

It's in great condition and the soundproofing makes a huge difference. I also got rid of its standard fans and added in a computer ATX power supply to power a bunch of Noctua fans with a controller to adjust their speed. It also powers all of my Raspberry Pis. Anyway it's very quiet.

If you stick to 4u severs, those are usually easy to quiet down as well. Otherwise many Supermicro server boards are standard sizes, you can put them in a large enough computer case and make it whisper quiet, this one's great for example: https://www.fractal-design.com/products/cases/meshify/meshify-2-xl-dark-tempered-glass/dark-tempered-glass/

Dell/HP/IBM/etc tend to use proprietary board layouts which will not fit in a standard case unfortunately.

Stay away from 1 or 2RU servers, nothing can make those things quiet.

Anyway if you just want a cool server and have no space for a rack, I'd recommend going the Supermicro board + Fractal meshify case route and just shove it under a table or something.