Laf I wanted to take pic from difficult angels. On digital cam,on the screen, you can see what camera sees. So you can put cam on floor and take pics. etc Plus now I know there is lot more to photography then a camera. SO A small half decent digital cam would do just fine to get any one started. I am thinking about getting one too.
Besided the Nikon D5000 that PandyaPhoto recommended, you should also check out Sony Alpha 300 and 350 or the newer, soon to be released 330 and 380. All these models have LiveView and an articulating screen. What Sonys do not have is video, which Nikon D5000 does (720p @ 30fps).
You should also consider Canon T1i, which has LiveView and video but no articulating screen.
The Sony's can be had for $600-$700, the Nikon for $850, and the Canon for $900. (All prices include kit lenses).