Well, according to specs, you have a PCIE x16 slot inside the PC. So YES, you can upgrade the graphics. You can buy any GPU you like, choice is yours. Just click over to the graphics comparison charts here at Tom's Hardware and see what's powerful enough for you, then check around to see how you like the prices. Three things to keep in mind:
1. Basically any graphics card will perform better than the integrated solution you have currently. You don't need to spend a mountain of cash to see the difference. But if your PC is second-hand, make sure it wasn't already upgraded. If it was, then you might not see a worthwhile boost in performance, depending on the card that might have been installed. If you have the PC from new and didn't upgrade it, then you are running the weak integrated graphics, and an upgrade will help a LOT.
2. Don't buy anything from the top of the charts. Your processor is not hefty enough to let a high-end card stretch its legs. The card will perform around the mid-range mark, so simply go for a GPU from somewhere in that category. This will give you the same performance for much less money.
3. And yes, you will need a new PSU. Look for something with decent reviews and from a known brand. If you don't needlessly buy an over-the-top GPU, go for 400W, 450W maximum.