I don't think you need to specify any Intel since you asked for 'most of the modern processors good for gaming' because anything 'cheapest' will not fit all that much of Intel's processor line since Intel cripples processor support with sockets and chipsets. Even when you get into somwhat more expensive boards...or the most expensive Intel boards...you still can't fit as broad a selection of their gaming processors.
You can put any Ryzen or Athlon AM4 processor in that cheap motherboard...even Ryzen 3000 chips when they come available later this year. That just not something you can do with Intel boards. The only thing excluded would be Threadripper, but that's arguably not 'good' for gaming as it's a workstation processor.