I would definitely recommend consumer grade hardware for a small home server, I ran older server gear (dual e5645+42GB ram) and found it to be loud and power hungry, especially at idle. Moved over to only slightly newer consumer stuff (i5-3470+8GB ram) and it still did what I needed it to, without costing $40AUD a month to run.
8GB of RAM is perhaps a bit limiting at times but I’ve not yet run into any critical issues because of it. I wouldn’t want to try simultaneous, high bit-rate transcodes on it but aside from that it’s been fine for my use case.
Have you considered some kind of remote mouse app? There’s multiple good options out there, wifimouse.github.io/ for example