I was thinking of painting a golf ball for my dad for fathers day because he loves golf and has a shelf to put golf balls on. Does anyone know what kind of paint would work best to put on golf balls?
Any specific kind of brush you recommend?

You should be able to use the small bottles of modeling enamel. Clean the ball with alcohol or paint thinner and keep your bare fingers off of it.
Go or call to a driving range and ask what paint they use to mark the balls to keep people from taking them.