you can get the gobbue mount when you are lv.30+ in Limsa outside, not playing atm so dont know exactly where but you have to talk to yoshi............. um, the wandering minstrel to get him, I personally would try for this mount first just because 2.0 is almost here and after 2.0 you won't be able to get it anymore.

Your chocobo mount you buy with grand company seals at the grand company you join for 3,000 grand company seals, In order to join a Grand company you need to do the first 5 starter quests for each Grand Company, after that you can join one and buy your chocobo.