If you want to avoid blurry photos (fuzziness), here’s a quick list of things to look for:
1) An image stabilized lens (also known as IS or vibration reduction)
2) A large max aperture lens (such as f/2.8, f/2.0…the smaller the number the better for your purposes)
3) A camera with low image noise to enable high ISO speeds
For Sports: A high zoom range to enable easy close-ups in sports (but beware that zooming in too much makes hand-shake more prominent, as others have told you). Image stabilization helps with this greatly.
Ignore cameras with digital zoom; this will not enable sharper zooms in your photos, but will instead just effectively crop the image. Also check out this website's page on
understanding camera lenses.
Don’t pay too much attention to the megapixels. Around 6 should be plenty and I would not recommend looking for higher unless you are doing so because the camera happens to have some other feature you want. When you have a better idea of what you are looking for, you might also want to look at dpreview.com to evaluate a few different models.
Hope this helps get you started.