https://pcpartpicker.com/products/video-card/#c=373,392,391&sort=price
$230-250USD gets you a 4GB RX 570/580, or a 6GB GTX 1060. Given the choice, I'd recommend the latter right now.
https://pcpartpicker.com/products/cpu/#k=4&sort=price&page=1
$115-170 will get you an FX-8350 or 8370. You have to consider a couple of things, though:
1. Is an FX-8350/8370 compatible with your motherboard? The maker's website should have a list of compatible CPUs for your particular motherboard, if it's not listed in the manual. so you should double-check that it's the actual CPU (i.e. FX-8370
<> FX-8370e: the former is the regular CPU, the latter is a downclocked model with a lower TDP).
2. Do you really want to replace your CPU with another FX CPU when you're already at end-of-life on the platform? The FX/Socket AM3+ ecosystem is "dead" in the sense that there will not be any future CPUs manufactured for that platform (just like the Haswell/Socket LGA 1150 & Skylake/Kaby Lake Socket LGA 1151 platforms from Intel). If you can afford it, you could consider upgrading to a Ryzen CPU -- a nice Ryzen 5 1400 system with 16GB of RAM runs you just over $400 USD (https://pcpartpicker.com/list/pZ9pnn), call it $650 with the new GPU. That compares to $360-400 for a new GPU & an octa-core FX CPU.