Which CPU for home / game servers?

I would like to put together my own energy server that is as energy efficient as possible.

I would choose Proxmox as the main operating system and then run at least two virtual machines on it. One should be used as a file / media server (then also 24/7 active, Linux with possibly Nextcloud and Plex), and the other as a game server (mainly Minecraft, with mods, only active if also used, max. 5-10 players, Linux).

I was thinking of buying an old used Xeon processor, but you can't be sure how well virtualization works and how energy-efficient it works.

Since the CPU is the basis for finding a suitable board and RAM, I ask you what your experience is and which you would recommend these days (if possible a specific one, there are so many to choose from that I can't make up my mind 🙃)

I was thinking of buying an old used Xeon processor, but here you can't be sure how well the virtualization works

As long as the CPU can do VT-x and VT-d, what you plan to do will work.

how energy efficient he works.

This is rather the crux of the matter. Usually: the older the CPU the cheaper, but the more power it wants.

In general, you can look at L Xeons, ie CPUs whose designation ends with an "L" at the back, these are the low voltage things that need little power. But be careful there too: little is very relative, depending on the model series.

In order to be able to recommend something, a budget would be very helpful.

I would say budget for everything up to 200 euro. Doesn't want to spend too much on a home server now. Something to start with that I can upgrade later if necessary. Do not have much experience with it and would like to familiarize myself with it ^^

Now sounds like less demanding requirements.

Have you ever considered getting a single board computer, such as Raspberry Pi? Let a MC server, TS server, file server and two self-programmed games with multiplayer function run over a 4GB Rasp and everything will run wonderfully! Even really energy efficient thanks to the ARM architecture!
Maybe the cheapest option if you don't have a lot of experience and want to try it out first!
For example The MC server managed 25 players without any problems!
Modded is not a problem I think, although I have not tried it yet, but should also run (to increase the RAM from 2GB to 3GB for the Java VM)

If you want to familiarize yourself with it first, are VMs on your PC not good for you? Most hypervisors can nested virtualization, so you can e.g. In a VM Pack your Proxmox and start VMs there again.

Otherwise it might make more sense for the budget to look for a complete sheet, e.g. With Gekko or ITSCO or stop Ebay and then the CPUs look up whether the power is hungry or not.

You can't virtualize on ARM stuff.

Unless that is a tough requirement, a handful of pis are definitely a good and very cheap alternative to such a x86 cogeneration plant.