The minimal amount of VRAM is not that important, but keep in mind that VRAM can define how big may be the framebuffer. For a 1920x1080 display with 32bpp, it means that one screen takes about 8 megs... so to be on the safe side, 32 megs could be the absolute minimum (about 4 screens).
If you're using a modern Windows (post XP) or a suitable Linux, it's more important to have some kind of media acceleration (like IDCT and those things) than VRAM. Some web browsers and plugins may benefit from offloading some work to the graphic card (hint: those porn videos), but this capability is only present in modern OSs. If you're not going to see HD videos, forget about that.
I have traveled across the universe and through the years to find Her.
Sometimes going all the way is just a start...
I'm selling some stuff!