After the scenes in Luca, you will end up on the Celsius, the airship of this game and the base of the Gullwings. You’ll also be given control of Yuna, if that matters. Anyhow, speak with Buddy on the port side of the bridge and you’ll be given an Al Bhed Primer , used to help you learn the Al Bhed they’re speaking sometimes. Also speak with Brother - in the pilot’s chair - to get three Al Bhed Primers from him.
Also be sure to speak with him again for the Festivalist Dressphere! That’s about it here, item-wise. The Festivalist Dressphere is most noted for its quick-to-learn Confuse ability. If you played Bravely Default on the 3DS, you’ll probably know the utility of the Confuse ability: in that game, for example, you needed the Confuse status on a specific enemy to learn White Wind. The same is true here: as you battle throughout Chapter 1, keep an eye out for White Wind and Mighty Guard abusing enemies; Confuse them and you can have your Gun Mage (the Blue Mage of FFX-2) learn these invaluable, invaluable skills.
Speak with Rikku, Paine, and Shinra (the unusual-looking kid at the computers), too, if you want. Speaking with Shinra actually yields some useful tutorials. After the one about Garment Grids, you get the Vanguard Garment Grid , too! Head up the stairs to the south and use the Save Sphere to, like FFX, heal your HP and MP and to well, save! Go further along to the elevator and head to the Engine Room where you’ll find some chests on the lower level - four Potions, three Remedies, four Phoenix Downs, and an Ether .
Return to the elevator and head to the cabin. There, you’ll meet the Hypello barkeep, aptly named Barkeep. Stock up on some items if you want (and if have the Gil). 5-10 Phoenix Downs at least is a good idea. You won’t see any particularly problematic enemies in the next dungeons so there’s no particular need to buy accessories. However, be sure to sleep in the upstairs beds to achieve 100%.
As you return towards the elevator, you’ll hear an alarm sound; head to the bridge and speak with Buddy. You will be notified that Mt. Gagazet seems to have a sphere in its floating ruins and that’s apparently important. Go.