Picking a digital camera, a specific purpose?

I often get see eye-candy and I want to take a quick picture of it or I need to take memos so I need also a screen to look back at them.

I need the camera to:
- Boot quickly (point and click for an instant picture)
- Mediocre shutter speed
- Digital with Screen, to review/view photos
- Focus (otherwise 12pt text is all blurry, smudged and I NEED TO READ IT)
- Physical size smaller than an iPhone (I won't keep it in my pocket)
- I don't care for screen Size
- Mediocre battery life, I only take or view 0-3 photos a day
- Cheap price
- Robust (if I knock it by accident I don't want it to shatter into a gazilion pieces, like iPhones do)

Anyone can recommend me something? Maybe someone used something like this in the past.

Maybe the Nikon P7800 would be good for you. It is small enough for street photography (eye-candy) and has a voice recording feature to document what you want. IOW, take the photo, review it, record a 15 second audio.