These balls are a little different to finish than a lot of other projects. Most people fill a jar with their choice of finish, dip the ball or soak it for a short period, and then hang it to dry with a fish hook on a string or whatever. You have to be careful that your finish doesn't gum up if not removed from the surface of the ball.
Avoid finishes that need to be wiped off or otherwise removed from the surface of the wood before drying
Formby's Tung Oil Finish - This isn't 'tung oil', but instead is a varnish blend. It works fairly well and is readily available.
Lacquer - This is fine for a single level ball. I use Masters brand.