You have 5 sets of 19-20 main scene quests you must complete which are under the titles of:
A Realm Awoken [awards ilvl 70 blue items]
Through the Maelstrom [awards ilvl 90 items]
Defenders of Eorzea [awards ilvl 110 items]
Dreams of Ice [awards ilvl 110 weapons/armor]
Before the Fall [awards materia and tons of gil]

Here's the link to the site:

http://ffxiv.gamerescape.com/wiki/Ma...A_Realm_Awoken