Party members: Badger, Ultimecia
BGM: Final Fantasy I Town Theme
It's your first town! And FFI veterans should recognize it in a heartbeat: it's Cornelia, that lovely city, that paradigm of civilization, that...well, it's actually pretty boring, but it does have shops, and that's a plus at least.
Gold Needle, 200
Echo Screen, 120
Phoenix Down, 500
Sleeping Bag, 500
Stock up on a few Potions and Antidotes. In this early stage of the game, you may want to conserve Ultimecia's MP for Thundaja, so stocking MP-free healing isn't a bad idea, even though she has Curaja. You'll have ample use for Antidotes once you start encountering Hornets, so stock up now while you can.
Amusingly, Cornelia sells exactly the same weapons as it does in FFI, although no character you ever recruit will use the Nunchuck, Knife, or Rapier, and the only character that can use the Staff comes equipped with a weapon that is many times better. Naturally, Badger has a Hammer already, so unless you're one of those completionists who just has to have every item no matter how useless, you can skip going to this weapon shop altogether.
Aha, finally, a good place to spend your money. Both characters can upgrade to Power Armlets here, and Badger would be well-advised to trade in his Collar for a Floppy Hat. Not only does it offer more protection, the images associated with it are hilarious. You afore-mentioned completionists, however, should beware: there is only one plain Collar in the entire game, and Badger comes equipped with it! You won't need it for anything throughout the game (ever,) but if you plan to finish the game with a full item list, hold onto that Collar.
Although Badger expects to head to the castle in proper RPG fashion, Ultimecia points out that that's pretty stupid when she's trying to avoid attention. This is merely a rest stop on the way to the real destination: the Chaos Shrine to the north, which Ultimecia can use to jump back into the timestream.
That's right. No castle-visiting for you. If you try to go in, the guards demand Light Warrior identification, and when Badger can't produce any, he gets rudely escorted off the drawbridge. Stupid guards.
Once you're done fooling around, leave Cornelia and head further north to the hulking, foreboding shadow of the Chaos Shrine.