If these are outdoor shots with plenty of natural light, most digital cameras will do a good job of taking action shots. I would look for a camera that also has manual controls. That way, you can pick the shutter speed.
If you also want good action shot under artificial lights, you need to look at DSLR (digital single lens reflex) cameras. These start at about $650 for the camera body and lenses start at about $80.
DSLR camera bodies can exceed $4,500 and some lenses exceed $10,000.
I have used a Canon 20D and got excellent results with action shots. It is priced at about $1,500 with a 50mm f1.8 lens.
In continuous mode, the 20D can fire off over 5 photos a second.
Perhaps you should set a target price before we make recommendations.
I'm interested in finding a digital camera suitable for taking mainly action shots. What is the fastest camera on the market at the moment and/or which cameras have the best options for taking action shots?