Go on eBay, punch in the price you're looking to spend and search for an old server. Keep in mind some manufacturers use proprietary connectors.
Look for servers with lots of ECC ram, clean photos of the internals.
They probably won't have a drive that's pretty common.
To meet that 16 core requirement, you'll probably be looking at older dual socket systems.
Edit: a quick search I found this. https://www.ebay.com/itm/225978893065?
Not a perfect match but the price is pretty good.