Question I have 2 parts, how do I maximize my bang for my buck?

Nov 27, 2020
Hi forum! So in quarantine i discovered the wonders of a gaming pc by using my mothers pc that she uses for her job, which in essence is a nice build that works great for gaming. Only problem is, now Im addicted and wanted to create my own pc.
Now Im trying to make a pc that can play Valorant/Csgo on 240 fps on 1080p whilst streaming. I bought an x570 mb and a ryzen 3600x. Should I upgrade my processor to a 5600x since its gpu demanding or is it enough for what I want? Furthermore, what gpu is good to buy? In essense, out of all the benchmarks and investigations Ive done those types of games arent thay demanding on your gpu, so I should be able to get away with buying an rtx 580. I only have around $500-600 left to invest so Im in a standstill on what I should do. Please help gods of pc building. Oh, and I know that my mb might be overkill, but I want to upgrade my gpu in the future, and Im willing to invest in cooling so I can OC.
Thanks if you read this far!