i7 3770k 1080p gaming, AAA titles, Ultra settings (Highest possible, no RT) ** GTA V, Shadow of the Tomb Raider, etc **
RX580 8gb used OK upgrade, 30% avg bottleneck & 40-60fps
GTX1660 Super used solid upgrade, 36% avg bottleneck & 50-70fps
GTX1660 Ti used solid upgrade, 37% avg bottleneck & 55-75fps
RTX2060 used solid upgrade, 37% avg bottleneck & 58-88fps
1080ti used better upgrade, 35% avg bottleneck & 75-90fps
2080ti used even better upgrade, 37% avg bottleneck & 90-100fps
A list of provided GPU's in this thread for reference point.
I'd hunt for a used one within your price range that supports DVI connection, can go new depending on the model you're looking at.
If you're ever planning on going to 1440p, I'd suggest looking for a used 2080ti but also consider your PSU when looking at these GPUs as well.
GL