Does it have to be the 9600? iirc the B580 works with 10th gen. I'd guess you're probably not buying new but the new prices of the 9600 and 10600KF are very similar on PCPartPicker. On ebay it looks like you can get a used 10400 for only a little more than a used 9600 (admittedly I don't typically buy used so I could be missing something there). I don't know about compatible motherboards though.
If you can't make it work for the B580 then a 2080 for $200 would offer excellent price to performance, though you may find yourself limited by the 8 GB VRAM before too long. If you can find a 6700 XT for no more than $260 or a 2080 Ti for no more than $275 that would offer about the same price to performance as the B580 (based on TechPowerUp's database of relative GPU performance). Knock about $30-40 off those prices to have price to performance on par with a $200 2080.