First, usually Starmie is used to rapid spin. But Starmie is pretty frail and can't switch in on neutral hits very well. You'd like to give it Cosmic Power or recover to help that problem. But then attacks are needed otherwise Starmie is pointless. Do you use Thunderbolt/Ice Beam? What about Surf? Then Psychic and Grass Knot are also good moves, so is HP Fire.
All Starmie needs: - Hydro Pump/Surf for STAB. Always. - Ice Beam - Thunderbolt - A choice moveslot. Recover for staying power, Rapid Spin if you need it, or an additional coverage move like Psychic, a solid secondary STAB attack and an answer to nearly all Fighting-types.