please help us find our perfect little digital camera

[domu221]

Another suggestion for under US$500 would be the Nikon P510 which would be one of Nikon's top of the line compact cams.

Based on the things you need:
It has a continuous burst mode of 7 frames per second.
1920x1080 full HD video at 30 frames per second.
ISO100-3200 (with a Hi setting of ISO6400)
and you have a lot of flexibility in terms of adjusting exposure (as well as learn a lot from this camera) with modes like Aperture priority auto and Shutter priority auto for that DSLR feel.

You also get some bonuses like a:
Viewfinder (Digital)
16.1 Megapixel CMOS sensor
GPS (for geotagging)
Flipout screen (can be both an advantage or disadvantage)
Manual White Balance adjustment
42x optical Zoom, NIKKOR Extra Dispersion glass lens with Vibration Reduction (very impressive zoom with very impressive glass and very impressive VR for less shakey shots)

It might be a disadvantage for you if you prefer traditional cameras that are rectangle-sized. This one takes the shape of a dslr (but smaller of course).

 

[rockandroller]

P510 looks like a beautiful camera, but we need something that can be in the pocket at all times...

currently leaning towards a smokin' deal I found locally on Canon ELPH 500 (IXUS310).. at 4x2x1 inch, i think its the biggest camera we can manage.
(I'd love to have something half as thick, but not many contenders out there with aperture 2.0 )

 

[rockandroller]

Followup: bought the ELPH 500 (IXUS310). At $168 it was the best deal locally available. Tested today, and results are encouraging.

1) outdoor pics VERY SHARP, colors very good, indoor shooting very good
2) battery life - got 256 12mp pics, plus 8 1920x1080 short video clips (total about 5 minutes) before low battery warning. The canon spec claimed 220 pics, so I'm not disappointed.
3) 3MP burst mode works great, its firing off about 8 frames per second continuous, I tried a couple bursts of ten seconds or so, it didn't fill up, or slow down. Focus is excellent.
4) video quality is EXCELLENT, really sharp, good colors, smooth playback
5) screen is EXCELLENT, very sharp, and I was out in VERY BRIGHT FULL SUN for an hour today, and had no trouble whatsoever seeing the screen, even though the brightness was on the default ( 3 out of 5). I can contrast that starkly with my OLED samsung 'camera-phone' where bright sun made the entire screen invisible...

Caveats:

1) the P mode continuous shooting is disappointing, as it only manages about 1 frame per second at any size (I tried 12 mp, 6 mp, 3 mp...). Seems you get to do that as long as you want, but it's nowhere near the published spec ("approximately 3.4 images per second"...) That's using a Lexar Professional 600x UHS-116 meg card which my card reader could access at 35 M/sec

2) as reported in most reviews, the touch screen is not very responsive. Maybe 1/3 the reaction of my cel phone. I'm getting better, but it's still a pain to get it to click or drag when I want it to (and running the calibration didn't help much). Not so bad I would dump the phone, but certainly 'takes a lot of getting used to'!

 

[gryffinwings]

The only thing I can think of that would probably fit the bill is the Nikon J1 and V1. The have the FPS and video to boot, it's a little bigger than a PnS camera, but it has better performance from what I know. However you are going to spend a little more than $500, consider it a camera that you can expand with.