if you don't know anything about camera's a SLR may be overkill.
for generic pictures of the family, kids, etc. a more compact, or even sub-compact camera might prove more fitting.
I have a Nikon Coolpix P80 that is more than adequate for the vast majority of "non-art" types of photography that our family needs - and best of all I don't have to explain how to use it to the wife, and even our kids have been able to get some decent shots.
speaking of which, the built in sports mode, and movie mode combined with the 18x optical zoom make it pretty versatile for a sub $300 camera. it's being, or has been phased out, and the replacement is 24x optical zoom and even higher resolution.
<-- decent comparison sight - there are many out there - this one covers quite a bit of the market and even includes various sample images at several different resolutions, as well as easily allowing you to line up various camera's side by side to compare features, and links over to owner/user reviews as well.