After conducting some research and concluding that I have an AGP 4X/8X slot on my motherboard I decided to purchase a GeForce 7600GT with 256MB video RAM.
I spent most of my time at ExtremeTech and Tom's Hardware. This article sealed the deal. While it was written with an emphasis on gaming, I found that my setup was so antiquated that the options were few.
I ordered it from NewEgg and it will be here tomorrow.