If you are purely looking for fun, I would not suggest ballet. Ballet is very strict with a huge emphasis on technique. Sure it is beautiful, but it is WORK.
Modern can be fun, but it is so closely connected to ballet technique-wise that it could possibly be less fun for a beginner. It is probably more suited for somebody with previous ballet training.
Jazz is an extremely fun form of dance. Although there is emphasis on technique, it is much less strict than ballet. Jazz can be done with or without "tricks" and most beginner classes only require a pirouette or a leap and the rest is high energy, happy, jazz-y dancing that anyone can do if they have the right attitude!
Hip hop is also a very fun form of dance as there is no technique involved whatsoever! If in a hip hop class, the emphasis would be totally on performance quality through facials and energy. If you have the energy, attitude, and some natural flow, you can be the best in your class or even your studio with a little work!