Used PCIe HBA cards pulled from retired servers can be found on eBay for ~$50. They have external facing ports and/or internal facing ports. External is the way to go if you're using a small form factor PC like a business class Lenovo. These are almost all low profile cards, so they will fit in any SFF PC with a PCIe slot. There are special cables which will connect one port on the card to four SATA- or SAS-based disks.

The PC's PSU will need SATA power on its cables or else you'll need to scavenge a separate PSU and use the paper clip trick (or better yet, a purpose built connector) to get it to power things on without a motherboard connected.

Once you have all of that, then it's just a matter of housing the disks. People have done this with everything from threaded rod and plastidip to 3D printed disk racks to used enterprise JBOD enclosures (Just a Bunch Of Disks, no joke).

Total cost for this setup, excluding the disks, can easily be done for less than $200 if you're patient and look for local deals, like a Craiglist post for a bunch of old server hardware that says "free, just come haul it away".

Check or r/DataHoarder on reddit or ServeTheHome's blog