I would upgrade the power supply, RAM and graphic card.
You need more Watt to feed a better Graphic card. Not that the new one will make the system use more then 350W, but a Pwersupply should never use over 80% of it's maximum capability.
- It can damage the PSU and components.
- The efficiency decreases a lot.
A bronze validated 600w Power supply would do wonders and increase the efficiency.
Get a complete new set of RAM. Mixing RAM is never a good idea.
Then the best Graphic card we can find for the rest of the budget.
I'll make a recommendation in a minute. I have to do something now. i am at work