Digital cameras: Please help me find a FAST P&S!

Please help me find a FAST P&S!

Hi! I could really use some help finding the right camera. I'm a mom of 3 (2, 3, & 11 years old), so I need a basic point & shoot compact to ultra compact digital. I've been doing HOURS of research and banging my head into the same walls. I can't find any site to rate cameras by my interests, so I'm hoping someone can assist me by reading my needs and recalling what cameras could work best.

Things I want/need in order of importance from most to least:

1. Speed! I need lightning fast speed because I'm always missing moments due to slow startup, time from hitting shutter button to actual photo taking, time it takes to zoom in and out, and time in between pictures.
2. Size. I would prefer the smallest camera that has the most of what I'm looking for (so I can slip it in my pocket or purse).
3. Picture Quality. I'm not really particular, but it'd be nice to have something like Image Stabilization or Blur Reduction or something that actually helps because my current digital often takes blurry ones.
4. Decent movie mode (minimum 640x480 at 30 fps) with acceptable audio. And it'd be really nice (although not 100% necessary) to be able to zoom during movie mode.
5. Good maximum storage upgrade (like 2GB or better yet-4GB).
6. I'd really prefer a USB connection as opposed to a cradle.
7. Pretty good battery situation. I'd prefer AA, but a long lasting (like at least 300 shots) rechargeable would be acceptable.
8. Decent wide angle for the occasional landscape I like to take (again, not necessary-just nice).
9. Rugged and weather resistant would also be nice, but it seems Olympus has the corner here, and I'm not too keen on what I've read about their speed!

Things that you might think I'd care about but don't really:

1. LCD display. As long as it has one, I'm not too picky about size or quality. I mean a nice 2.5-3" would be super, but not necessary at all.
2. MPs. Since just about everything is above 5 MPs anymore, and all I'm doing is emailing and making normal size prints, it's not a huge deal either.
3. Brand. As long as the camera works, I'm not worried about names.
4. Price. While I can't afford a really expensive camera, about all I'm looking at retail between $249-499, which is acceptable.

I really appreciate whoever read this whole thing and can actually help me find what I'm looking for. If I could search by criteria like shutter speed, image stabilization, and all those other important things to me, I wouldn't be asking for help. But there are SOOOO many cameras out there, and I'm having a very difficult time finding what I need. Thank you very much!