How To Improve Item Level

[Jeeqbit]

I go to complete the quest "Rock the Castrum" and cannot enter it because my item level is only 36 and 42 is required in order to proceed.

Always open the Character window and click the Recommended Gear button. This automatically equips the best gear in your armory chest (which is where most of your quest rewards and dungeon loot probably went).

The only ones I have found in shops are also junk.

Every main city has a market place -including Ul'dah - Sapphire Avenue Exchange, Limsa Lominsa - Lower Decks and Old Gridania. You can speak with the Battle Armor merchants and there is gear for all levels. 1-9, 10-19 and so on. DoW since you use physical attacks.

You can get high-quality versions of this gear from the market boards too. These are where players sell the items instead, but they can be a lot more expensive.

I noticed you are a Lancer, but have Dragoon unlocked. Note that equipping your Soul Crystal turns you into a Dragoon, which unlocks a lot of new abilities. If you do all of your Dragoon quests, you get a coffer you can "use" that gives you item level 90 gear.

As you get Allagan tomestones of poetics from this content you're about to do, you can spend these with the Blue Icon NPC just outside of main city aetherytes, for item level 130 gear, which will last up to level 60 quests.