Hello, I'm a new Proxmox user. I'd like to set up a Quake III Arena server. Can anyone help me with this? Best regards.

From PVE's perspective, q3ded is an application for a Linux host as any other. So you just set up an LXC container or QEMU VM with a GNU/Linux distribution of your choice in it on PVE, make sure it's properly available on the local network, and then install your application inside it. That's probably the harder part to get right, but also *highly* off-topic for this forum

I suggest you check out running a server for CPMA/ProMode (https://www.playmorepromode.com/) or ioquake3 (https://ioquake3.org/) instead of id software's original Quake 3 Arena; both are excellent continuations based on the GPL'd free software release of Quake 3.