Which camera to purchase.

Choose an important game, and hire a photographer for the event.  Sports photography, especially indoors and when you don't know what you're doing, is nearly impossible.  If "average" is lousy, that's what you can expect if you try to burn money on a cheap Canon dSLR kit with an f/5.6 lens, and add to that a total lack of experience.  Even at the semi-pro level, you're talking about ISO Speed 3200 at f/2.8.  Anything less, and you need a camera with ISO Speed 6400 or faster, preferably with an f/2 or faster lens.  Daytime softball is easier, but you still have to know what you're doing.  Sports photography isn't going to work by spending $500 at some discount sale.  If you don't want to hire a photographer, or you can't due to availability, then it's time to spend money if this is important to you.  You need at a minimum:

Canon 60D or 7D

Canon 85 f/1.8

Canon 200 f/2.8

Monopod

32 GB memory

Lots of practise

I'd throw $500 at a photographer for two games, and then no worries about screwing up or having to buy something that I didn't intend to use much and wasn't really interested in learning.

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http://www.alexanderrogge.net/arshutterbug