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