I am in no way knowledgable on photography or cameras, but I too have v. young kids and found that I kept missing the "precious moments" because the kids don't
always ever hold the pose, and shutter lag was causing me to get the pic just too late.
So I'll steer clear of recommending any cameras as my knowledge is limited, but from practical experience I'd advise you get one that has a low overall shutter lag (especially for when they start to move!)
Maybe some of the more informed can give you pointers....
(I went for a Sony DSC-S600 as I wanted a basic point and shoot and it's fine as long as the batteries are fully charged)
Edit: This table helped me with my decision:
http://www.cameras.co.uk/html/shutte...omparisons.cfm