What CPU is good for RX6600XT?

Currently I have Ryzen 5 2600 + RX6600XT + 16GB of RAM (2400mhz, very slow) + old mobo with PCI-e 3.0 I want to upgrade my base (cpu, ram and mobo) so it matches my GPU. My CPU is now more often doesn't fit into the minimal requirements for new games and it gives me a headache in some old ones (cpu based), like Battlefield 2042, CS2, Helldivers 2, etc. I was thinking of something like Ryzen 5 5600 or Ryzen 5 7500. What are your thoughts and advice? I am willing to spend 200-250$ at most. I don't hesitate on buying used parts.