Verne,
The spec you're looking for is defined as "Shutter Lag Time". My Fuji has a 'rapid start-up time' of 1.1 seconds and a 'shutter lag' of 0.01 seconds. I don't see that spec listed for the Canon S3 IS on the dpreview site but I'm sure you can find it on another site somewhere. (Maybe Rick can find it in his User Manual.) You can reduce the lag time by partially depressing the shutter button for a pre-focus, then waiting for that 'Perfect Instant' to snap the shot.
The Canon does accept rechargable AA batteries, both in Ni-Cd and Ni-MH. They list a "Battery and Charger Kit (CBK4-300) under "Accessories". Actually, the camera doesn't know the difference. They just suck the juice from whatever is in them.
(And the MSRP for the Canon is $499...... but you can beat the He!! outa that price!!! Just ask Mr. Murphy.
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