My vote is also on Proxmox. I also started out with a mini PC about 6 months ago and installed proxmox. It has a few quirks regarding its disk usage you have to get used to, but its UI and setting up of VMs and LXC containers is so simple, you do not need any manual. You can easily build and tear down linux machines and play around with them. You cannot run docker images directly, but I use an LXC ubuntu container to run them, works flawlessly.
Oh shit, I remember there WAS a game. I believe I bought a Geforce 2 MX or sth for it…could have been an FPS, possibly Unreal Tournament.