Is it possible to upgrade

The Intel Core 2 is still a good CPU, although it's starting to get old. Throwing in a GPU would be the way to go, without knowing what power PSU it has in it I'm not sure what to recommend. I'm thinking it's probably got their 325w PSU, so a 7750 would be good.

Can I upgrade the PSU as well? How much do you think it would cost to get the 325w psu and 7750 gpu and would it be difficult to install them?

PSU are good for people to install when they just start working on computers. It's takes a good, i don't know 20 minutes, helps get you used to doing stuff in there. I think you'd probably be pretty happy with the 7750, but you could step up to a 7770 too if you want to buy a new PSU. My 7770 will max out WoW.

Here's a good PSU to buy, this will handle a 7750, and a 7770, but not much more but that's why it doesn't cost so much. http://www.newegg.com/Product/Product.aspx?Item=N82E168...
People really like that VP series.

Here's some GPU's for you to look at too, as well as a benchmark between the two:

http://www.newegg.com/Product/Product.aspx?Item=N82E168...
http://www.newegg.com/Product/Product.aspx?Item=N82E168... (I have this same card, it's an excellent choice)

Benchmark: http://www.anandtech.com/bench/Product/535?vs=536

Thanks!