Sounds like you have one of those mini-ATX type cases that was pushed really hard by HP and e-Machines brand a couple of years ago.
You might have a problem with the overall size of a video card going into one of those PCI slots but you never know till you buy it. If you are only looking for a "band-aid" to help you get by for a while then just buy the PCI video card. However if you are wanting to get something with a little more spring in its step then get a new case, mobo, CPU and AGP video card. Make sure you keep reading up and decide for yourself which card you want based on how much you can afford.
As a general rule of thumb I don't upgrade my entire system every year. I upgrade pieces over a two year period. My next system upgrade will be a CPU/RAM/MOBO but that will not happen till at least next spring/summer. By then the 2.5GHz+ CPU's will be cheaper and will give me a huge jump over my 1.4GHz T-Bird.