Depends what your focal length is. If you're shooting at say 50mm (35 mm equivalent), then you'd like to keep your shutter speed to atleast 1/50 of a second. For 60mm, 1/60 sec, 100mm, 1/100 sec. Even moreso with a P&S, since they are so small, I find them harder to stabilize in my hands.
More than likely though, even with a cir polarizer in bright sunlight, you'll be sittin' pretty at 1/200 or higher most of the time.
