The camera I would recommend is the Sony P200. The best price from a trusted store I could find online was about $10 less than the Kodak you are considering, so it seems in your price range.
It is the only small camera that doesn't produce much red eye because they managed to move the flash away from the lens a little.
Shutter lag and cycle times are excellent: http://www.imaging-resource.com/PRODS/P200/P200DATA.HTM
It has a great movie mode and takes excellent images. It is small enough to carry around easily and has a hard protective cover over the LCD. It has a continuous focus mode so you can get nearly zero shutter lag with pre focus. Flash range isn't great but it is about the same as you C50 was.