I'm upgrading my PC, I'd like to know where to start

You have a very weak graphics card in the 6450. I'd recommend a GPU upgrade. What is your budget and what monitor resolution do you want to run?

Your system has a 350W power supply, which could run a Radeon 7750 just fine. If you want to go with a higher end video card, you will need to upgrade the power supply to 500-600W as well.