Couple simple questions..

[Conradus]

You don't quest for a chocobo, you purchase it with GC seals once you are officially inducted into a Grand Company. When you can start a quest depends on the quest; some are available at level 1. You can become a GC recruit and do the first GC quests at level 22, but official admittance as a Private Third Class (required in order to purchase your chocobo) will require level 25. You may rent a chocobo from the rent person in each major city once you level any class to 10, no quest or other requirement imposed. Your current class doesn't have to be 10 as long as you have a class that is.