How do I progress?

[Archona]

Get 1 piece of loot from CT. If you're a fresh 50, do not be picky, just get one piece your class can use, and worry about the order for further weeks later.

Buy your Grand Company ilvl 55 weapon (or use your relic precursor).
Run CM until you have most of your Darklight armors on the left side.
Run WP after that to finish your Darklight jewelry set.
Start on your relic quest, pick up a weapon from Ifrit HM, Garuda HM, or Thornmarch.
Finish relic quest.
You can do Ultima, not required though.
Begin Coil once you have at least full darklight + relic weapon.
Begin Extreme Modes.

You can craft HQ ilvl 70 items, but its generally not worth it. The materia prices can break your bank, and Darklight is satisfactory anyway. Prices may vary by server.