Speed is an issue with most compact digital cameras. They've improved a lot in the last two years. But shutter-lag and slow shot-to-shot time are still a fact of life. If you've had trouble with these things in the past, you should be looking for a faster camera. But be aware that they'll pretty much all be better than a camera that's 2 years old or older. And really, camera technique is the most important thing. If you know what you're doing, you should be able to get good photos of your kids and general action with almost any camera. IYou need to know your camera, its limitations, and how to get the most out of it.

Hope that helps-