Abin Sur's Lantern and Eye of Ekron with its power damage mod set the base just like any Controller.
Qward Gambit brings some much needed team utility with its power life-steal aura and group shield, as Starro has no shield and can only heal himself when he creates a minion.
Fatality's Energy Lance provides a strong poke with its Active that ties into Starro's Parasite to increase the damage you can deal to a single target.
Lobo's Chain significantly enhances Starro's ability to ensure a Parasite stays on a specific enemy, also making it easier to land his other skills or Artifact effects against them. The extra HP takes advantage of Starro's ability to quickly heal himself with his passive by giving him a greater reserve to heal. Hook Shot from the mod solidifies his ability to lock down and kill a single target. Take this over Atlantean Royal Seal as the additional attack damage benefits from the extra damage against enemies with Parasite, and being that Starro has only 2 damaging skills, 1 of which already slows the enemy, the slow from Royal Seal is less beneficial.
Amulet of Isis improves Starro's survivability and Will and the team speed boost from Mercury's Gift ties in to the boost Starro can give his minions with E. With this item, Starro, all of his minions and the rest of his team can all rush forward at once.