Quartz Extreme needs only 16 mb of gfx memory (32mb recommended). Browni, I'd be very surprised if your machine didn't support QE. There's a little utility somewhere to see if QE is working.
Also, if you have a DVD drive, you can watch a DVD movie in a window (in the middle of your screen) and adjust the volume or screen brightness. If the speaker (or sunburst) graphic shows up over the movie, you're running Quartz Extreme.
32 MB is recommended, but apparently you can run QE with 16 MB RAM. My test is, when you have the background set to change, does it just change, or does it transition? If it transitions, if one image fades into another, then you have QE active.
Go for either a Radeon or a GeForce 4; it doesn't matter a whole lot which of either you get, as they all have at least 32 MB VRAM and provide excellent 3D rendering and QE support.