But...You didn't mention a price range.
Without a price range, we tend to go overboard.
With more information we can offer better suggestions:
Any preferences as to camera size (shirt pocket, jacket pocket, or full size camera)?
Do you need a zoom larger than 3X ?
What type of action do you have in mind?
looking for the above for my wife, whom is interested in capturing our children in action -- good or bad; her main goal is simply getting the shot the easiest way possible; however, from my standpoint, i'd like to have pictures that can actually be blown up into usable pictures...any suggestions?? thanks for the help