I am not a keen photographer as such but wish to be able to take good quality photo's of my daughters Gymnastics, which means indoor sport photography with no flash, and to be fair you are always a good 20 - 30 m away so zoom lens needed.
I have a Sony a200 with Sony lenses but it really does produce noisy images. What is the best option a low f-numbered lens zoom i.e. fairly expensive or a better camera with normal zoom lens.
Can anyone suggest the best option and if it is the camera which one I should opt for sub £1000

Hope this makes sense, many thanks. Mark