Your design system should also include a style guide. It picks up the visual style guide (colours, typefaces, logos and so on) along with the usage rules for each element. For instance, knowing when red should be used, when typeface #1 should be used, and so on. Before starting this work, prioritise the elements that recur most across your product, such as buttons or navigation elements (menu, footer). Once your base is solid and properly built, you can move on to variations and other elements. Remember to test your “parent components” (the main one, used as the model) before building “child components” (variations of the main one).
Still with a view to improving communication and work between developers and designers, it’s important to name your components properly. Each element should be named in lowercase, with words separated by hyphens. This convention gives developers elements that are easy to implement. Start with the letter representing the atomic-design level (a for atom, m for molecule, o for organism, and so on), then the type of element and its variations.
Example for your primary button: a-btn-primary. Be careful to name components based on their function, not on their form (colour, shape, visual style). Don’t forget that your style guide will evolve. Example to avoid: a-btn-red.