If you want to shoot sports you might want to resign yourself to the idea of spending good money on good glass up front. You don't learn auto racing in a VW beatle. Sports photography is one of the most demanding disciplines in photography, not only on the photographer, but on the equipment. I shoot sports and I do not own a lens slower that f2.8 for two reasons. 1. There are many occasions I need fast glass for low light venues. 2. I want the DOF control that only fast glass provides. The difference between a sports snapshot and a good sports photograph is isolation of action. This is accomplished by sharp focus from sharp glass, good framing and shallow DOF that has just the action in focus leaving the foreground and background people and artifacts out of focus.
If you do not want to spend the money on the Canon 70-200 f2.8 Version I or II then the only lens I would recommend is the Sigma 70-200 f2.8. A little higher than what you want to spend, but a lens that from my own experience, will be pretty well up to the task. I have the Canon in my collection, but a friend of mine that shoot High School Sports uses the Sigma and he gets the job done with that lens. Of the mentioned 3rd party lenses it is the only one I would recommend.
One last thing to keep in mind when buying good glass. Good glass holds it's value much better than cheap glass. If you decide later on to upgrade or change photographic directions you will get more of your money back with good glass.
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