I answered you over there, and I'll add more here.
First, "good pictures" is very subjective. You might have lots of people tell you they get good pics but when you look at them, they might not seem good to your tastes, or the tastes of others, though they're fine for them. Many times when you see sports shots, especially those indoors, they are blurry, or out of focus, etc..
Sports are notoriously one of the most difficult things to shoot in photography, especially those that are indoors. Why? Because of the movement/fast action, the distance, often low light, etc. The photographer and the camera need to be able to capture the action in a fraction of a second to get a decent shot.
Note I said the photographer as well as the camera because more often than not, it takes knowledge to get there; the camera alone won't do it by itself.
Think about what you see professional photographers using at sports events - dSLRs with big, honkin fast lenses that are in the $5000 range. And even then, it's not always enough. One year at a summer tournament I was taking pictures beside one of those photographers who had a big, honkin zoom, using my older dSLR and a relatively slow lens. (Hadn't aquired a fast tele for sports at that point yet.) Well guess what? Most of my pictures came out better than the ones he took. How? Well, lots of reasons. But the most important one being practice and attention to detail on my part. In most of his pictures, either appendages (like tops or heads or limbs) or equipment (like bats, gloves, hats) were "amputated", i.e. cut off, and views of the players were generally unflattering. Mine, OTOH, included all appendages and equipment in shots, and were generally flattering to the players, simply because I knew them and I knew their routines, and I'd been photographing them at that point for years already, etc. The other guy was clearly rushed.
My point being that equipment alone does not make great shots, photographers do. Now I know someone will come along and say that equipment is indeed important, and of course, it is. Ideally, you have a good photographer and good equipment - no surprise the two together will yield the best shots.
You also ideally have to know how exposure works, and to that end, reading Understanding Exposure will go a long way.
So you need to get a decent dSLR with modern specs and a fast lens or two. Obviously, this isn't done cheaply. Fast lenses can be quite expensive. (The fast tele I have costs about $1300+ but I got it used for about half that. I have bought many lenses used and have had great luck.) An advantage with beginning or learning with slow lenses helps you understand what you need in a fast lens (i.e. it's part of the learning process), but it's not absolutely necessary. You'll also need a tripod as well, which keeps the camera still to eliminate shake as a factor in blurry shots.
This is just scratching the surface, really. There are so many factors that need to be considered when getting into this. I'd probably google sports photography or photographing gymnastics or low light sports and see what recommendations come up. It's a lot to digest, and you need to ask yourself what you're comfortable doing and how much you want to spend, etc. HTH. I will PM you the name of a poster who went though this not too long ago who may be able to help you more.