The quick capture is the hard part.
Only in the past three months have the manufacturers made headway in shutter lag time.

When you press down the shutter button, first the lens has to focus and only then will it take the picture.

The auto focus time has been almost a second to over a second on many cameras. This time is getting reduced on the newer cameras.

The way to get around this for action photos is to press the button half-way down to let the lens achieve focus lock and then wait for the action to happen, then press the button all the way down.

You should look at the Kodak LS743 (4 megapixel) and the LS753 (5 megapixel). They seem to fit the description you listed. Their total shutter lag time is approximately 0.4 seconds. That includes focus time.