For most artists, it's going to be just you in terms of ownership and no employees. Life is complicated enough, so just keep it simple. Many artists will find that the sole proprietorship, the simplest form of business, is going to work just fine. There are no official papers to file to form a sole proprietorship.
The OSBDC offers many free workshops for people looking to start or grow their small business in Oklahoma. The Oklahoma Visual Arts Coalition is another organization dedicated to fostering talent and creative entrepreneurship in our state. Check out their Business of Art workshops here.