Sport Coach looking to buy a video camera

I'm coaching a high school track team and I am looking to get a video camera to assist with coaching... I honestly don't even know where to start. I guess I'll give you an idea of what important to me.

Good quality, doesn't have to be 1080p, but I need good quality
High Frame Rate, people are moving fast so...
**Frame by Frame Play Back supported on the camera**
**Composite outputs, hdmi output a plus, want to easily be able to play back on a tv**
Large screen, I want the ability to play back on the camcorder itself
** easy to use**
good battery life
large hard drive/whatever type of storage it has

Budget is around $500 bucks, but I want something good so i might be willing to pay a little more if nessesary.

Thanks so much in advance for any help in locating a good digital video player.

P.S. frame by frame support and slow motion is an absolute must!