@declandoom your computer has an integrated on-board graphics processor (card). Yes, you can upgrade with a PCI card. Now this is where it gets interesting. Depending on which model your computer is (mini tower/small form factor or USFF) will make the differnedce in which form factor your graphics card must be to fit . The small form factor only allows for low profile cards. So you need to look for one that specifically states it is low profile and includes a low profile bracket. MT supports full height card, DT supports low profile card. SFF supports low profile card.
Regardless of form factor, one of the better ones would be a Radeon HD7750 but the Radeon HD 6450 with DP and DVI as well as a 512MB Radeon HD 6350 were offered as optional cards for your system. So those may be the best choices. Once you determine what card you are looking for, make your determination in regards to the PSU.