Abin Sur's Lantern and Eye of Ekron provide a good all around boost to Zatanna's skills, the mod on Ekron's improving her damage as she gains more Will.
Olympus Gambit ties into the power armor provided by her passive, granting an attack and high power armor boost, in addition to slight HP regen, to all allies, making up for Zatanna often using her shield/heal as offense. The Will regen from her passive makes up for the lack of Will on the Gambit. Additionally, in the time Punish/Protect is cooling down you can make use of Bastion, reducing the damage the enemy does for a few seconds before you blast them again.
Qward Gambit grants a bit of power damage and the life-steal aura provides Zatanna with a bit of additional healing between Protects while also benefiting allies, the Protection Field providing a large deal of survivability both for herself and the team during fights, allowing her to still shield the team while she Punishes enemies. The mod buffs Zatanna's damage a little while giving a good boost to her and allied power life-steal.
Atlantean Royal Seal improves her power damage and grants additional health to take advantage of her higher armor values. With Skewer having a very low cool-down and targeting an area, combined with the large AoE of Punish, the slow from the Seal provides a significant increase to her crowd control, allowing her to Dazzle a single target or slow an entire group.
Amulet of Isis gives more HP to hide behind her armor with, Will to increase her skill scaling and damage due to Eye of Ekron, and a bit of extra mobility. Mercury's Gift ties into the Dash side of her Dash/Dazzle skill, allowing her to grant a team-wide speed buff, either to ensure a timely escape or to secure a kill against an enemy she Dazzled.