Theoretically, memory speed is probably the most important thing (since most intensive 2D operations involve copying and/or combining large buffers), although the latency of the CPU-to-videocard connection is also important. RAM size can be an issue when working at high resolutions, although a 64+MB card is unlikely to have any problems at any remotely normal 2D resolution.
For all practical purposes, any card you can buy today is plenty fast for any 2D-only application. This was an issue when you had single-pipeline GPUs at 100Mhz with 8MB of 100Mhz RAM; the videocard is probably not going to be your bottleneck in any 2D app these days.