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This ought to get you started on some options. I picked features that I would consider critical (e.g. shutter & aperture priority, good zoom range, manual focus option, flash). The first two results look quite nice for that price range. Check out the Konica Minolta DiMAGE Z10 and the Olympus C-740 (which I'm pretty sure has been discussed here before, though the search is returning nothing). People here also seem to be big fans of the Canons, like the PowerShot A80, and some can probably give you more advice on them. Good luck!
The C-740 looks to be the most compact of those in the comparison I linked to. To stay in that price range and get into the compact or ultra-compact range, you'll have to sacrifice some features. There are still some good options, though. The DiMAGE F100 can be had for ~$300, it seems, despite the $700 figure on dpreview.com. (It is a couple of years old.) The zoom range isn't nearly as large as the C-740, and the macro focus distance is much larger (worse). But it's definitely much smaller than the C-740. Another compact option might be the Sony DSC-V1, though you're looking at more like $370.
Sorry, easy to get carried away when it's other peoples' money . Anyway, definitely check out the DiMAGE F100. It's quite cheap ($200 or less), and it has the bare minimum features that I would expect of a camera (manual focus, S/A pri, flash), plus a host of other nice features (good ISO range, good zoom, EV comp, movies, timer, optical viewfinder, and more). It takes SD, which I'm not a fan of, but if it meets your criteria, go for it! There are some nice samples here if you want an idea of what it's capable of (scroll down on the image page to get the original).
Nice. Just the 512MB will serve nicely, I'm sure; hundreds of pictures at the highest quality setting. The F100 will shoot at 2272x1704, 1600x1200, 1280x960, 640x480. I would guess that TIFF mode uses the max resolution and movies use the min (and jpegs at any of the sizes).