I quickly threw together a full parts list. The RX 580 is not actually $250, one can easily be found for $50-$100 on eBay, bringing the total price down to $475. It's certainly not ideal performance, but $500 doesn't go as far as it used in this RAM and SSD market. You might knock the RAM down to 8gb or the SSD down to 512 if you still need room in the budget for a monitor and peripherals
Buildapc
ddr4 is going for around $25 per stick of 8gb I went ahead with 4 sticks of 3000mhz
Not bad, I found a used mobo for $60 and I'm looking at ram right now on eBay. I'm hoping that I can get a higher spec GPU, just not sure what to go with. Sucks that storage is so high right now. I might have an ssd I can use though I'll have to check.
If you can find a good deal, the 1080ti the other guy mentioned would do you good. If not, the 1660ti (or 5600xt if you prefer AMD) go for not much more than the 580
Looks like a 1080ti is $150 so I'll grab one
Nvidia 1080ti and Ryzen 5 5600x is a pretty solid pairing that will run you a little over half your budget. I had the very same setup until about 2 years ago. You ought to be able to run anything pre~2021 on max settings without any issue, and pretty much anything afterwards with medium-high graphics (YMMV).
The GPU will be your bottle neck here but is about the most cost effective option. Consider upgrading it if possible
I found this combo with the 5600g https://ebay.io/m/icN0lD
Now that I'm looking at it I think it's just for the CPU and the seller is just dumb.
The 5600G is indeed a combo, but with integrated graphics. It's obviously vastly less capability than a discrete GPU like the ones mentioned in other comments, but would certainly provide you flexibility and time to find a good deal on a GPU
Although a 5600G isn't very good for gaming, it sure is convenient down the line when you repurpose the old machine as a home server.