Leaving the joists open saves cost, provides easy access to electric and plumbing. If the foot traffic from above does not bother you it is a great budget friendly option. The color is your choice depending on the style you want in the space. If you go with light colors on the ceiling texture will be a focal point. (Perhaps coastal theme ?) If you choose a dark paint (e.g. black) it hides the details and imperfections yet provides an interesting industrial like look, but you can make the room the focal point. The dark ceiling however, gives a feeling of lower ceiling height so if you have 7' ceilings keep it in mind. Free hanging ceiling light fixtures could further "hide" the joists visually. Good luck with your project. Cheers.
Q