Now would that work good for like close up shots?
That depends on how far away you are from the object. When shooting a school football game 70-200 will be enough on a small stadium, but if you're gonna shoot at large stadiums from far away, you might actually need 500mm like the previous poster showed he had.
Another thing is the camera itself. If you have 12megapixels, you can only crop so much to make a full photo. If you have 21 megapixels, you will be able to crop a lot more.
I am not a big sports photography fan so I may not understand why you'd need 24mm wide angle for sports, maybe only if you're trying to take a shot of the entire stadium or something? But for general sports and close-ups, I think something like 70-200 is pretty good as far as the focal range is concerned.