I am not a big fan of the Sony ''W'' series of camera and their twin counterpart; the P100/150/200.
They have a very short shutter lag (0.2) seconds. They have an excellent lens and take great photos, but they all have a quirk.
During low light shooting (with and without flash), the camera will select a slow shutter speed. Too slow for reliable shooting. Any camera movement will result in blurred pictures. You can compensate by switching to manual mode and selecting a faster speed.
But that can lower the light for the exposure.
Of the cameras I listed, I would rate the Kodak 7440 and Z730 as the best choice for people with kids who move too quickly for most digital cameras. Those cameras have a very short shutter lag (0.2 second).
Plus they have an excellent lens.
For versatility and good photo quality, the Canon A95 is tops for the price. People love that swivel LCD. The shutter lag is not as good as the Kodak cameras mentioned above. Shutter lag is 0.6 second.
If you are looking for an ultra thin camera, the Canon SD300/400/500 would be an excellent choice. Great photos, great movie mode and low shutter lag (0.3 seconds).