Many thanks for all your good advice.
My ping isn't too bad. According to speedtest.net
London, Paris & Berlin, plus pretty much every central European country: 40ms
Moscow and Athens: 60ms
New York: ~120ms
Johannesburg: ~190ms
Beijing: ~240ms
Jakarta: ~260ms
Sao Paulo: ~290ms
This kind of latency is something I can live with because I live in Europe and my friends live there.
I don't plan to run it on Wifi. It's going to sit next to my router (or somwhere close) connected via Ethernet port. It's safe to be concerned :)
RAID is something I should consider. A drive running 24/7 is bound to fail at some point. Not like it would be the end of the world, it's just a game server after all, but still. I have two 500GB HDDs with me at this very moment, and I can source something from work too, so I'll give it a thought.
As for watercooling and piezoelectric cooling: I truly intend to source all of my parts from work if possible, and we just don't deal with stuff like that. AIO liquidcoolers are occasionally available, but they don't actually make coolers any quieter than standard ones.
I don't care about desktop applications for the CPU. It only needs to run a dedicated server for gaming without graphics. Anything else is "nice" but totally unnecessary.
For aesthetics, I don't care. If it's just a bare PCB sitting in my drawer, or a smashed up laptop smeared with latex paint, then I'm fine with that.
Gaming
