You just hit level 50, well now what? It is time to start progressing the ilvl of your gear to take on the end game content. Here is a brief outline guide on what you will be doing.

When you hit level 50 and complete your Main Scenario Quest, you gain access too:

Castrum Meridianum - 100 Allagan Tomestones of Philosophy per clear.
The Praetorium - 100 Allagan Tomestones of Philosophy per clear.
The Wanderers Palace - ilvl 60 loot.
Amdapor Keep - 80 Allagan Tombstones of Philosophy and 40 Allagan Tombstone of Mythology per clear, as well as ilvl 60 loot.

Weapons
1. Grand Company - Bought with Company Seals, should be the first thing you get
2. Primal Weapons - Ifirit < Titan < Garuda (Yes, Garuda's weapon is better than Titan's).
3. Relic - A long quest chain starter in Vesper Bay.
4. Relic+1 - Costs Allagan Tomestones of Mythology after you get your Relic.
5. Allagan - Drops from Coil of Bahamut.

Armor
1. Artifact - lvl 45 and 50 Job quests, this armor is essentially given to you to get you started.
2. Amdapor Keep/Wanderer's Palace - Loot armor.
3. Darklight - Costs Allagan Tomestones of Philosophy.
4. Artifact+1 - Costs Allagan Tomestones of Mythology. (Do not bother with this gear until you have your +1 Relic Weapon).
5. Allagan - Drops from Coil of Bahamut Dungeon.

Amdapor keep is where you want to start due to the fact that the armor drops will be better than your AF gear, and you get both Tomestones of Philosophy and Mythology. Tomestones of Philosophy can be exchanged for Darklight gear and Tomestones of Mythology can be turned in for Artifact +1 gear from NPCs in Revenant's Toll. Remember you will need 900 Tomestones of Philosophy for your Relic weapon, and 900 Tomestones of Mythology to +1 your Relic Weapon. Getting your +1 Relic is the most important thing and you should not be using Mythology on anything but that unless you have more than 900 to spare.

Once you have hit your weekly cap of 300 Tomestones of Mythology for the week, the best way to get Philosophy is to spam Castrum Meridianum runs. Yes, it is boring, but it is the fastest way to gain Tomestones of Philosophy to purchase Darklight gear.