Well, except for the "bulky" part, the Panasonic FZ-10, with very fast 12x optical zoom lens, would be ideal. Barring that, the next choice would be the Canon S1-IS, smaller but with 10x optical zoom. Both of these cameras have long zooms and image stabilization so that you can pull off those long action shots, even on cloudy days. The S1 IS offers a pretty good movie mode for those soccer victory films. The downside is it takes a lot of memory so you will have to spring for a fast, large, memory card.
Both are priced under $500, and will yield good prints up to 8 x 10. Give em' a try. After that there are a ton of ultra zooms from Kodak, Fuji, Olympus, etc., without image stabilization, in your price range.
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