I've been using the Canon series for a while. SD300 and 800IS. I like the Canons because they have good color in their photos, are quick to turn on, quick in shot to shot, have VERY easy menus, so you can make adjustments very quickly. For instance, I found the Sony menus too deeply layered, and it took me too long to navigate to what I wanted. Not as familiar with Fuji or Nikon.
The downside with all tiny cameras is red-eye, noise above ISO 200 (that is, starting at 400) and some lens vignetting and distortion. Also, they generally don't have great zoom. The Canon SD series also doesn't have any manual control over aperture or shutter speed. They do in some Canon A series. Not sure on Nikon or Fujis
But, for a camera you can put in a pair of tight jeans pockets ALONG WITH an extra battery, the SD series is great. And in terms of pulling it out, turning it on, making a menu change, and taking the pic, there really is no camera I've tested that is quicker.