Maine Academy of Gymnastics Team @ the Frostbite Meet
Exposure? If the gym has consistent light, I go 100% manual exposure after measuring a gray card for a custom white-balance and shooting some test shots around the gym. Unfortunately, many gyms are not consistent and I need different exposures depending on the area of the gym being shot. But still , manual gets me the best results as the exposure meters often get fooled by bright walls, dark walls, or even windows. At this particular gym, the white walls would have caused serious underexposure. Yes, I could have used auto-exposure compensation, but I've found that manual exposure works better. (See two shots below, the window would have really thrown the meter off).
The Still Rings
First of all, they aren't still, but the Rings are my favorite. The athletes have to fight off a tendency to sway and keep them still; failing to do so will make the dismount that much harder.. Technically, face recognition AF modes are useless most of the time since the athlete rotates so much. I tend to use a Dynamic 9-point setting and time the dismount after getting used to the routine.
Pommel & Mushroom
All I know is that I was NEVER that flexible at age 11 and 12. When I shoot the mushroom, the biggest challenge may be just getting a decent vantage point, after that it really helps to know the routine and when the athlete will do a "scissors" move. AF modes vary but for this I revert to either a Dynamic 9-point or single point and focus on the gymnasts core.
I find the floor to be the toughest to shoot: action is erratic and often running and spinning. One of those situations where you want a camera with a really good AF system.
The funny thing about these kids is that if you saw them in the movie theatre or at the mall, you'd have no idea how strong and flexible they are. Their training includes a lot of "strength" and as a result, they generally win any pushup or pull-up competitions at their schools. And they are generally REALLY GOOD KIDS.
Closing concept: Know your camera
So below is a snip from a very helpful web page Nikon created for sports shooting with a D5. They have similar pages for other cameras as do other manufacturers. All I can say is to seek this information out as it will save you a lot of trial-and-error time. Also note that in the multiple disciplines of gymnastics, your settings will likely vary by event. For me, the floor is the toughest. If they are taking their "runs" right at me, I use more of a "hurdler" setting with 9 point dynamic area AF. Otherwise I follow the chart below if they are going left to right. Rings and high bar are also very difficult as you will find focus shifting from face, to hand, to body to leg and back to face.