Fast fully automatic compact

[newaroundhere]

Budget

* What budget have you allocated for buying this camera? Please be as specific as possible.

$500, though flexible up or down

Size

* What size camera are you looking for? Or does size not matter at all to you?

compact

Features

How many megapixels will suffice for you?

I'm told 6 is sufficient, though perhaps 10?

* What optical zoom will you need? (None, Standard = 3x-4x, Ultrazoom = 10x-12x)

Not particularly important

* How important is “image quality” to you? (Rate using a scale of 1-10)

8

Do you care for manual exposure modes (shutter priority, aperture priority, manual)?

no

General Usage

* What will you generally use the camera for?

pictures of young children

* Will you be making big prints of your photos or not?

possibly 8x10s, probably not much larger

Will you be shooting a lot of indoor photos or low light photos?

yes

Will you be shooting sports and/or action photos?

Not necessarily for sports, but speed is very important - my wife hates lag between photos and really wants to be able to click over and over without pause (a la DSLR). Probably the feature she is most inererested in.

Miscellaneous

Are there particular brands you like or hate?

have always owned Nikon but not particularly focused on it

Are there particular models you already have in mind?

Have been told to consider the RX100 but that seems like potentially more camera than we need

(If applicable) Do you need any of the following special features? (Wide Angle, Image Stabilization, Weatherproof, Hotshoe, Rotating LCD)

No

And thanks!

[Andy Stanton]

The Sony RX100 is probably the best camera in the class of small point and shoot cameras with large sensors (for superior image quality). But it's quite expensive - over $600.
Similar, less-expensive cameras with large sensors and very quick shot-to-shot times are the Panasonic LX7, the Olympus XZ-1 and the new Olympus XZ-2. This website has not reviewed the LX7 but has reviewed the previous model, the LX5:
Panasonic Lumix DMC-LX5 Review

The website has also reviewed the XZ-1 and XZ-2.
Olympus XZ-1 Review
Olympus Stylus XZ-2 Review

If I had to choose among the three I'd probably select the Panasonic LX7 due to its combination of speed, features and image quality.
The XZ-1 is not as good a camera as the XZ-2 or the LX7 but it's currently available online at under $300.