I have about 10 years experience shooting pro-rodeo from inside the arena. The standard lens is a 70-200 f2.8 with high-speed focusing, either a Canon 70-200L f2.8 USM or the Nikon equivalent will be on 90% of the bodies. Rodeo action is extremely random and can change the distance to the camera very fast so having a fast focusing lens is essential.

I found using the center focus sensor, which is a cross-pattern, to be the most effective, because the random motion played havoc with the focus speed. By studying the riders I learned what part of them to track to give the camera the best chance of staying in sync; Basically you want to locate the part of their body that moves the least, which usually will be the trunk, from the hips to the shoulders. Using the center sensor means you'll have to avoid zooming in tight so you have enough room to adjust for unexpected changes in direction while tracking. Our reactions will lag behind their direction change so the added room in the frame will help you still get an image if something good happens - think about pro-football players twisting to avoid a tackler - their bodies and the resulting shots look coolest because of the change of direction.

In addition to tracking areas on the subject that don't move quickly, you also have to be aware of what in the image the camera uses to track focus. It likes areas with lots of contrast under the sensor so it can find edges then it tries to make those edges as sharp as possible. Try focusing on a monochromatic (i.e. white, gray or black) wall and the camera has a hard time. Put a pattern of vertical or horizontal lines and it does better. Make the pattern into blocks/plaids/paisleys and it does it easily. So, you have to watch your subject and try to find areas where there is a good change in contrast that doesn't move fast. Gets challenging some times, especially if the light levels are low or there is lousy contrast. :-)

An AF-S lens would be a lot better than a standard autofocus lens for action. There is a lot more sophisticated focus mechanism in the AFS lens allowing you to zoom as you focus. With the cheaper focus you will end up fighting the zoom which really affects your percentage of keepers.

Also, while a prime is lighter and potentially able to capture more light because of a bigger aperture, they can be a pain for sports or fast action, especially when it's moving toward you. A good friend of mine has one of Canon's 200mm f1.8 lenses and we'd shoot side by side. I'd be able to pull out on the zoom and go to 70mm when he'd be stuck at 200mm shooting action moving toward us. He'd get a face or chest shot and I'd get horse and rider, or, I could selectively get the face. So, having the ability to zoom quickly and accurately maintain focus (because of the AFS or USM) was very important.

Regarding firing bursts to capture action - you'll find that the pros who are trying to get the peak action rarely rely on motor drive. It's ALL timing and knowing their sport. I have 9 FPS available on my Canon body and never use it except for messing around because it sounds cool. I've done tests to see what sort of granularity 9 frames a second gives me, and it misses a lot of motion. Figure it this way, 9 frames of 1/1000 second shutter speed gives 9/1000 of a second captured, leaving 991/1000 of the second missed. Your reactions are better than that, plus if you know the subject, you can really narrow it down. So, rather than mash on the button, study your subject, track it (panning) so you have the greatest opportunity for stopping the motion and being ready if something interesting happens.

Finally, aperture really has no bearing on how fast the camera can track focus in normal conditions, though it seems like it would. The camera doesn't stop down the aperture until it's ready to open the shutter, allowing it to have the maximum amount of light available to it to determine focus. You can test this by selecting a f22 aperture, then turning the camera around and looking down the barrel. You shouldn't see the blades closed down unless you release the shutter or press a depth-of-field preview button. Maximum aperture does come into play in low light. f1.8 is one more stop

The focus drive (USM or AFS) makes all the difference. You pay more but you get more. The lenses are better built, can take more abuse and are a pleasure to use.

And, when they act up they can REALLY piss you off, especially when you're expecting them to be working correctly, but we won't talk about that.