Have you looked into AMD EPYC?

There are regular deals comming from china with Supermicro Motherboard/CPU/RAM deals:

https://www.ebay.com.au/itm/134674563486

A setup like this will be a power hog though.

To control it from another room you would use the web interface of whatever OS you are using eg Proxmox. To turn it on you can use Wake On Lan commands/apps on your workstation/phone.

Check out a build video for an EPYC system here:

https://www.youtube.com/watch?v=aCrldtj9bGY

You have to make sure the cooler you use is rated for the CPU though:

https://www.youtube.com/watch?v=v0jZ12U3u4A

Im running a Dual 2690 v4 setup , 30 ish disks , 22 ssd's and 1tb of LRDIMMS in it. ran me about 2200CAD total not including the disks.

usually sits around 260w with a 15-20% load. disks set to spin down (only ssd's active usually).

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just parted it together with eBay and local stuff I could find.

Are you sure you need that many cores? You can overprovision the light duty VM’s if they aren’t all heavy duty.

You might also want to consider a 2nd hand workstation with dual cpus like the HP Z840 or equivalent from Dell or Lenovo. They are usually quieter than a rack server and should be within your budget and specs.

Keep in mind number of cpu cores isn’t a very accurate or complete measure of cpu requirements, 30 - 50 cpu cores from 10 years ago vs 30 cpu cores from current gen cpu’s is significantly different

I'm fairly curious as why you need "30-50" CPU cores and .. 64-128 GB RAM and to think about what you actually need before making decisions.

I run a "lot" of VMs as well, in fact, I naively migrated a bunch of other smaller servers onto this one because it's OP!!!!!
My main compute server is an HPE Gen 10 with 80 cores and 128 GB RAM and ... I max out with "most", if not all of my VMs on at once around 10 to 15% until it crashes because I'm out of RAM by a doodoo ton.

50 cores sounds pretty overkill for 128 RAM, in my humble-pie opinion.