For this type of build I was hunting for the cheapest possible CPU that was available on Amazon. There are some models cheaper than my selection, but they’re Intel Celerons, dual cores, and non-gaming specific chips. The
Ryzen 3 4100 is the cheapest option that I’d even consider for a gaming PC. It’s not fast, only has 4 cores and 8 threads, but it’s at least built on a solid AMD architecture and it’s on the AM4 socket so there’s room for easy upgradeability.