What types of pictures will you be taking? Portraits? Landscapes? Sports pictures? Indoor or outdoor? Really think through what your area of passion is with regard to photo taking. The answer to this question will help you determine which features are important for you.
If you'll mainly be taking snapshots of your children, you'll probably want a camera with face recognition feature and easy red-eye reduction. On the other hand, if you're always trying to capture action shots from your son's soccer game, you'll want a camera with high-speed burst shooting.
If you're like my daughter, you'll be snapping shots of beautiful flowers and other nature objects using special effects and more. You'll want a camera with some manual functioning and macro capabilities.