This has been an ongoing problem for me. I don't know a lot about cameras, but as you, I'm trying to figure this out.
Recently I viewed some basketball game pictures a fellow parent took, that were able to stop the action, and were still bright and colorful. He had manually set his aperture to 1.8 with a 1/250 exposure time. I was excited about this revelation. When I got home, I quickly pulled out my Olympus 700, and played around with the manual settings. Unfortunately, my camera's aperture settings would only go down to 2.8. I tried some sample pictures this morning (with my daughter bouncing her basketball in our bright florescently lit garage), and unfortunately had marginal luck with the 2.8 setting. The best combination I could come up with (on my camera) was 2.8 at 1/50 shutter speed. I'll try it in the gym, but I think my solution will unfortunately need to be finding a digital camera that can go down to the completely open 1.8 aperture(to provide enough light), an adequate zoom, and a minimal delay between when I hit the shutter, to when the picture actually is taken. At this point, I don't know what cameras can do that (and I'm on my 6th digital camera over the past 10 years).
If anyone out there has suggestions for me or "badexposure", please respond. I, too, would be very grateful.