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I think brunerww gave a well-thought-out answer, but I'd like to toss in one other option–a DSLR. You'll find some pretty good ones in the price range you stated, and they have the advantage of being small, light, and pretty easy to learn. Their biggest disadvantage is in sound–DSLRs do a lousy job of recording sound, and most shooters who use them either record sound separately, or they use a field mixer to improve sound quality.
However you shoot, don't rely on your camera's microphone. Audiences notice sound quality, and even a modest investment in a decent microphone makes a noticeable difference.