Ironically, the cheapest ballpoint pens typically work the best -- I've had the best luck with the disposable plastic Papermate blue ballpoint pens. Blue is preferable to black.
Sharpie Should not be used on a baseball. In the case of a baseball a Blue ballpoint pen would be most preferred, and recommended over a sharpie. Sharpie is not used for signing baseballs because of the porous properties of the baseball will absorb the ink and the signature will tend to bleed into the cover of the ball. Blue ballpoint ink has proven to hold up better over time against fading than other colored inks as well. Sharpie would be most preferred on a bat or photo for example, where the signature will stand out more.
When having a photo signed in sharpie be sure to allow the ink to fully dry before handling, and placing it in a protective plastic. If the ink is not completely dry the ink will smear. If the sharpie signed photograph is kept in a plastic protector, keep in mind that if the conditions are not right the signature could sweet onto the plastic.
Keep the signed baseball in a ball cube or case with at least 50% UV protection if you plan on displaying it. The Ideal conditions for display would be indirect lighting, at a room temperature of 65 - 70 degrees, and 50% humidity. Always check your signatures periodically for signs of fading or deterioration, and avoid excessive handling.
For more information on signed baseballs read my newsletter "How Much Is My Autographed Baseball?"