While talking about what makes people unique, let's not shy away from skin color. This basic characteristic is one of the first things children notice. My generation was taught to be "color blind." Unfortunately, this was a disservice. This is not a cookie-cutter world. We are all different. There is huge variability, even among those who consider themselves part of a group like "caucasian" or "black." The message we need to send is not that we're all the same inside, but that we are all different, inside and outside - and that's great!
A wonderful book, The Colors of Us, explores and celebrates the many shades of people. It's a joyful story with food-related imagery that all children will enjoy. I suggest reading this to your class and having them talk about their own skin colors. Help each child find the beauty in their own colors. Then, provide paint in many flesh tones and have them paint self-portraits.
Don't be afraid to explicitly compare and talk about skin color. Doing so in respectful and celebratory way helps teach children to appreciate, rather than ignore, the differences between people.