I checked out the specs on your computer, and it does have a single upgrade slot, of the PCI variety. Don't confuse this with PCIE, which is totally different.
To make it fit in your PC, some video cards come "low profile ready", which means the circuit board is narrow enough, and they include a narrow bracket for mounting in the slim computers. They leave it to you to switch out the bracket, which is usually a couple of screws. Pretty easy to switch out.
There is two major drawback to this suggestion:
- PCI is not the preferred connection for graphics cards (it has a slower interface, and thus lacks pretty much all more powerful cards).
- You may have to remove an existing card (a modem, or network card, perhaps) to make it available.
If you are a gamer (you want to play 3D games on it), I would hold off and save your pennies for a more capable machine. This is not it.
Otherwise, there are several acceptable (not great, but OK) low profile cards out there. Look for low-profile and PCI in the description. I know newegg has a bunch of different models available in the $35-175 range. Just make sure whatever you get is low profile & PCI.
That should get you going. Let me know if you have other questions.