I would look for a hp z240 with no hds and as much ram and processor as you can afford.

There are enough hdd slots to run a small nas or play with proxmox or both especially if you get to 32gb of ram or so. And in my experience the sffs upgrades are cheaper than the micros because right now that micro sodimm is pricey.

I keep scooping up Elitedesk 800’s for 100$ all day and then you can bump the ram to 32gb for the other 50. That gets you at the top of your budget for a pretty decent lil low power proxmox box

Did you try turning fast boot off in bios?