Hi there Wantfastercamera and welcome to the Q&A Board!
Is your 4.1 mp Cybershot the DSC-P73 by any chance? If so, it's considered a relatively fast digicam. Shutter lag is only 1/10 of a second when you're pre-focused and 4/10 of a second if you're not. 2.5 seconds is how long it takes from power on to first shot captured. That's actually not bad for a digicam.
Of the models you mentioned, the Canon SD500 is 1/10 and 1/2 second respectively. Power on to first image captured is 1.5 seconds. Not much of a difference. The Sony DSC P200 is 1.4 seconds power on to first shot, pre-focused lag time is about 1/10 of a second and 3/10 if you're not. Finally, the Sony DSC W7 is 1.3 seconds power on to first captured image, 1/10 of a second for pre-focused and 3.4/10 if you're not. Again, these are all considered fast.
(By the way, it's important to note that this data comes from
www.steves-digicams.com and
www.imaging-resource.com. Both are detailed reviewers.)
So, it seems that these choices are all similar. Now, you can improve your photo capturing response by leaving your camera on when you think your little one may be about to do something cute. That would minimize the missed shots due to power on delay. Also, you can pre-focus which will quicken your response time substantially.
Digicam lag time is something that requires a little bit of getting used to but once you've got that rhythm down, it'll become second nature to you. You'll be able to anticipate the action and accommodate it. Never missing a cute baby photo again.
