Take a look at the Canon SD1300.
It has a short shutter lag (0.2 sec).
So my Mom is looking for a new camera and I told her I'd help her track something down. Here's what she is looking for.
1)A semi-compact to compact camera. Doesn't have to be tiny, but a bulk SLR sized body.
2)A fast camera. The majority of her photography will be of her grandkids, who are all very young and moving. So she needs a camera that can take photos quickly and not have a long lag time between shots.
3) A good sized LCD screen.
I would say in importance, camera speed is probably number 1. Now I would like to add that my mom is almost 60 years old. i know many cameras will give you shutter speed options to get a faster shot, but that's beyond her capabilities. What she really needs is something very easy to operate with minimal tinkering and all of the extra features aren't really needed.