Fast glass means big aperture or
f/stop (which is counter-intuitive, smaller number equals bigger aperture, f/1.8 > f/5.6)
Fast glass (I think something like an 85 f/1.8 would be good for you if you go Canon) is generally more expensive, but allows more light into the camera so that faster shutter speeds can be accomplished (good for stopping action).
A used 20D and a fast prime (50 f/1.8, 50 f/1.4, 85 f/1.8, 100 f/2) would be a pretty good start. I'm not sure how close you can get in these agility events, but I'm guessing you can get fairly close.
Once you get into and start taking pictures you'll learn a lot faster. Good luck.