No, you don't need an air stone. You need two. Actually no system requires an air stone. We put them in because it will add more oxygen to the water, which will keep it from getting algae, and will make the plants grow stronger and faster. (A little.)

The only thing more difficult about an aero grow is that if you don't use proper filtration, your spray/mist heads get clogged. That project is not aeroponics because a spray is used and not a mist, which is even more difficult.

The easiest and most recommended for beginners is DWC.