You will get the first four pieces of your Artifact armour (Headpiece, Gloves, Pants and Boots) once you fully complete your level 45 Job quests. The chestpiece is gained at Level 50, once you complete your final Job quest. There's also a recolour/reskin of every Artifact set that can be bought by trading in Allagan Tomestones of Mythology by speaking to Auriana at Revenant's Toll, usually called Artifact+1, Relic, or gods know how many names there are by now.

As for items having a level above 50, there's an important distinction between the item requiring a particular character/class level to be equipped, and the item's actual level. The required level to equip an item usually has no relevance besides restricting you from using powerful equipment too early, while the item's actual level determines the item's power; the higher the item level is, the more stats it will grant when equipped. An item's level can usually be seen right above the Class tags on the equipment's tooltip.