Just a few words of caution if you don't mind; (You can check out reviews if you want to).
I will try to summarize my findings here;
I believe that most of the time, sport photography often requires high ISO performance. Well, the Nikon D200 is not very good at high ISO performance because it gets rather noisy at the higher ISOs. It's native ISO level is from ISO 100 - ISO1600 with ISO 3200 as boost. (Not very ideal in my opinion because the ISO 1600 is noisy).
You would want a camera with a good quality native ISO of ISO 200 to ISO 1600 at least (For sports). ISO 3200 might be needed for lower lighting conditions. It will depend on the quality of the ISO 3200. Special features like image stabilizations or big aperture prime lenses will make things far improved in such a situation.
Your Nikon D50 have a very good ISO performance even at the max ISO 1600. I suggest that you concentrate on getting a lens with a wider aperture (Fast lenses) and preferably telephoto primes because zooms tend to be rather slow at the long end. These lenses will be rather costly because of their quality, but in my opinion; it would be better to buy the lens than the Nikon D200.
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I am looking for faster focus, a better built/weighted camera body & more options for ISO/White Balance etc.
I will let the more experienced decide for you if the focus speed and ISO levels of the Nikon D50is sufficient or not. (Keep in mind that many dSLRs offers extensive WB controls)
Better build/weighted camera body is subjective, so I will let other people advice you further.
Regards. (Just my advice)
To ease things down a bit regarding theISO performance of the D200:
Sony A100 ISO performance = Nikon D200 ISO performance from ISO 100 - ISO 1600. (ISO 3200 on D200 is really noisy)