The more common elements that do get used in your public communications are:
A tagline is an important part of your brand identity. Here are some of the greatest taglines:
For guidance on creating a great mission statement, please watch this excellent clip from Fast Company:
And the story you want to tell needs to articulate clearly what you do, how you do it and why you do it. An excellent talk on the importance of "why" is found in this excellent TedX talk by Simon Sinek: