Unfortunately the manufacturers seldom put Shutter Lag in their specifications.
Some reviews of a camera will show the shutter lag.
A review of the A470 shows a shutter lag of 0.4 seconds, which is pretty good.
That is the time it takes to Auto Focus the lens.
The way to avoid shutter lag is to frame your shot and press the shutter button half-way down.
Then re-frame your shot and press the shutter button the rest of the way down.
That way the camera has time to auto-focus and you end up with a actual shutter lag of less than 1/10th of a second.
If you are using flash, another problem will cause a delay before taking a picture.
After a flash picture, it takes a couple of seconds before your camera is ready to take another picture.
The camera must recharge the capacitor that triggers the flash.
Their is no fix for this. Even $1,000 cameras have that problem. (Law of Physics).
The delay will vary depending upon how fresh your battery is and how far you are from your subject.
Usually, the first flash picture you take after turning-on the camera will have an unusually long delay.
That is because the flash capacitor is empty and it takes longer to charge up an empty flash capacitor.
The solution for that is to waste a flash shot before actually taking pictures.
Then you will have a flash capacitor that is at least half full when you start taking your flash pictures.
Camera makers can design the electronics so that the flash capacitor will recharge faster but that will cause the battery to overheat.
My wife has been happy with her Canon A470 for the past few years, but she's started expressing concerns about the time it takes between hitting the button and the camera actually taking a picture: so her and the camera's reaction time sometimes precludes getting the right photo as sometimes the "moment has passed" by a split-second.
So I'm looking into a replacement camera for her, preferably still in the same Powershot Axxx-level. My question is, what "statistic" should I be looking at to find a camera that takes pictures quickly? Is there a certain feature that'll be listed to cover that?