I know this isn't the answer you were looking for, but they're all the same. Arch, Debian, Ubuntu, Fedora, I've tried them all, and there isn't a discernable difference.

Will you use it for other stuff or just virtualization? Proxmox is designed for virtualization. It's based on Debian and has a web GUI.

It doesn't really matter that much imo. Virtualization is done by kvm or xen, both distro independent. Qemu, libvirt and anything else you might need will only differ version, which may or may not matter to you (probably not). Maybe you can gain some performance by building from source, whereas something like Gentoo might come out ahead... Then again, you can build from source on any distro so...

KVM with virtio runs circles around everything else

virtualization

Honestly, I don't know. Though, I'd reckon there would be any significant difference between distros.

stability

Depends on what you mean with stability. If you meant it like how "stable" is used in "Debian stable", then it would be any distro with a release cycle that chooses to not continuously deliver packages; but instead chooses to freeze packages and hold off updates (besides those related to security) for the sake of offering a relatively polished experience in which the behavior of the distro is relatively predictable. Some distros that score good on this would be Debian stable and openSUSE Leap. It's worth noting that Distrobox, Flatpak and Nix allow one to have newer packages on these systems if desired.

If, instead, you meant that the distro is less likely to break upon an update, then it's important to note the following:

• While you shouldn't expect breakage to happen in the first place, unfortunately it's realistic to expect it every so often (read: 0-2 times a year on non-stable distros).
• If you have a lot of packages, then it's more likely that at least one of them causes some breakage.
• Technically, every update is a potential 'breakage-moment'.
• Packages that haven't been installed through the official/native repos are more likely to cause breakage.
• Relying on Distrobox, Flatpak and Nix for (at least some of) your packages should benefit the stability of your base system.
• (GRUB-)Btrfs+Timeshift/Snapper allows one to create snapshots one can easily rollback to in case of breakage. Therefore it's worth seeking out a distro that configures this by default or set it up yourself on whichever distro you end up using (if it isn't included by default).
• So-called 'atomic'^[1]^ distros are (generally speaking) more resistant to breakage, but (arguably) they're less straightforward compared to traditional distros. It's still worth considering if you're adventurous or if your setup is relatively simple and you don't really feel the need to tinker a lot. Don't get me wrong; these atomic distros should be able to satiate ones customization needs, it's just that it might not be as straightforward to accomplish this. Which, at times, might merely be blamed on lackluster documentation more than anything else.^[2]^

As for recommendations you shouldn't look beyond unadulterated distros like (Arch^[3]^), Debian, Fedora, openSUSE (and Ubuntu^[4]^). These are (in almost all cases^[5]^) more polished than their respective derivatives.

speed

Most of the distros mentioned in this comment should perform close enough to one another that it shouldn't matter in most cases.

If you're still lost, then just pick Linux Mint and call it a day.

1. More commonly referred to as 'immutable'. Atomic, however, is in most cases a better name.
2. If you're still interested, I'd recommend Fedora Silverblue for newcomers and NixOS for those that actually know what they're getting into.
3. I believe that one should be able to engage with Arch as long as they educate themselves on the excellent ArchWiki. It might not be for everyone, though. Furthermore, its installation (even with archinstall) might be too much for a complete newbie if they haven't seen a video guide on it.
4. Ubuntu is interesting. It has some strange quirks due to its over-reliance on Snap. But it's worth mentioning, if you don't feel like tinkering.
5. With Linux Mint (and Pop!_OS) being the clear exception(s).

I jumped onto the FreeBSD train a year ago and needed some virtualization tool for my job. A started using bhyve and must say that I am quite happy with it and don't plan to move to any other tool soon. Not sure how it compares to other tools performance wise but it does the job for me.

Is this running in your main PC or a server type device?

Temple OS