Gear progression on Nocturnal Souls works something like this:
Equip and use gear dropped from enemies, bought off the auction house, or acquired through quests. You should have plenty of gil to keep yourself outfitted (remember to sell back what you’re not using). At level 50, you can begin acquiring your full set of artifact gear (main hand, head, body, gloves, pants, and feet) from the Artifact Vendor.
This does not prevent you from doing the Artifact Quests (AF1); however, keep in mind that not all quests may be working.
At level 60, you should not only have your artifact gear but now you can augment it using relic augments. Once augmented, this gear should hold you until 75.
The augments for these pieces tend to come from various NMs or collectible items, such as kindred seals. Again, the Artifact Vendor can assist you with the augmentation process.
Here you have your pick of two sets: your artifact +1 and your relic +1. In addition to your armor, the base version of your relic weapons become available at level 75.
Here you gain access to your relic armor +2 and empyrean +2 armor (and accessories), again from the vendors within the Celennia Memorial Library. Once acquired, the relic augment process begins again with rare/ex drops from Abyssea zones.
Congratulations, you made it! Here you begin reforging your prior relic, artifact, and empyrean gear into their final forms.