Have you taken a good look at the Fuji Finepix s602 zoom?
A friend of mine has it and takes nice actionpictures of her horse. It has a nice zoom too. It has 6x optical zoom, but it's also a pretty large camera.
I'll be buying the Nikon Coolpix 3100. It has a nice shutterspeed and the delay seems to be ok too. But it doesn't have the zoom abilities you seem to need in a camera. It does have a sportsmode, that takes, from what I have heard, very nice action pictures.