On a $315 budget from scratch, there is practically no room for a GPU.
- half-decent case, $50
- decent PSU, $50
- HDD, $75
- half-decent motherboard, $75
- half-decent CPU, $75
$325 already, still need a DVD drive, RAM, GPU, extra fans (optional), aftermarket HSF (optional) and probably a few other random bits if you had other customizations in mind.
You are looking at closer to $450 for something that can be called a gaming PC.