JME, I recently bought a Sony video camera that would suit your needs, (I shoot sporting events with it) but it was over $900.
This may be too late but when you go shopping ask one of the sales agents who knows his shit about shooting video with one of those small Kodak digital cameras. The are in the price range you mentioned.
We used one that cost about $130 on a ski trip and one of the kids posted it on YouTube and it was a perfect presentation. Plus this camera is small enough to slip into your pocket.
I'm sure one of these small digital cameras in the $200 range would be more than you would need.