I run a couple of containers on my lenovo mini pc. I have proxmox installed on bare metal and then one VM for truenas, one for docker containers and one for home assistant OS.

For me the limiting factor is definitely RAM. I have 20GB (because the machine came with a 2x4GB configuration and I bought a single 16GB upgrade stick) and am constantly at ~98% utilization.

To be fair, about half of that is eaten up by TrueNAS alone due to ZFS.

The point I'm trying to make is basically make sure you can put enough RAM into your machine. Some NAS have soldered memory you won't be able to upgrade. The CPU performance you need highly depends on what you want to do.

In my case the only CPU intensive task I have is media transcoding which can often be offloaded to dedicated bardware like intel quicksync. The only annoying exception is hardware transcoding of x265 media which is apparently only supported from intel 7th gen and upwards processors and I have a 6th gen i5... Or maybe I configured something wrong. No clue

Edit: I wrote that after reading the first half of your comment. Regarding connecting a screen, I think I had one connected once to set up proxmox. Afterwards I just log into the proxmox web interface. If required I can use that to get a GUI session of each VM as well.