It has a laptop style fan for the cpu. I’ve never noticed any noise but I have it off in a corner and near some noisy af parakeets so it’s silent to me.
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.
I’m using Jellyfin on a cheapo dell sff from shopgoodwill website. I hear you on the fragmented children’s content. The kids stuff was a big motivation to set it up.
What do you want to self host? To learn or experiment buy a cheap old x86 box. I get mine at goodwill auction. Otherwise desktop is good if you want something that needs more compute and that you’d spin up as needed vs always on.