Another vote for a ryzen 3600 - 3700x here. Don't even have to go x570 if you don't want PCI-E 4, but be wary of bios support.
As for GPU, that's the one part I've been sticking to buying used these days due to insane prices. Budget GPUs are leaving too much on the table for me performance wise, and high end cards are way too expensive to buy new. Your choice here will make or break the "gaming pc"..
I got a b-stock 980Ti which I run overclocked.. it's in GTX 1070 Ti territory and I barely paid $200 with a 1 year warranty (this was nearly a year ago, they go for much less on forum trades now). The 980Ti still runs every game in my library flawlessly (Borderlands 3 included at 1080P high settings, usually in the region of 90FPS. 120FPS on medium settings..)
So.. my budget PC suggestion would be
CPU: Ryzen 3600
Mobo: Pick your poison (Not sure when B550 boards are coming. Most b450/x470 boards will require a bios update for 3000 series).
Ram: 16GB Anything with SK-hynix C die, e.g. G.skill sniper 3600 (does 3600 at fairly tight timings for half the price of samsung b-die)
GPU: Used 980ti to as high as 1080Ti (unless RTX is a requirement). Vega64 is also VERY cheap in the US used and trades blows with GTX 1080 (non ti), but be wary of loud blowers and high power consumption/heat.
Note: If the monitor you're using is only 60hz/1080P, you could step down the video card even further. Point is, don't be afraid of used, prices came down a ton on the used market this year.
Sup. I like computers. Are you a computer?