Edgar: South through the cave, and eastward to South Figaro. We'll then make for the Returner headquarters in the north. Return to the castle and pass the word along.
Soldier:
Do I look like I can burrow through the goddamn sand or something? Understood, sire! Take care!
Final Fantasy games tend to swing pendulum-like between "detailed character customization system" and "static character mechanics with better-defined character development".
Final Fantasy 3 introduced the job system with interchangeable, nameless characters.
Final Fantasy 4 had static you-learn-X-spell-at-Y-level improvements with characters that developed over the story.
Final Fantasy 5 refined the job system and allowed skills to be transferred between jobs for the first time, but characters didn't really develop more than "adventurer", "princess", "Mary Sue", and "pirate who is also a princess".
Final Fantasy 6 swings back the other way. It's basically Everyone Gets Character Development: The Game, but each character is stuck doing their own special ability for the entire story (with one major exception to be found in the middle of act two). Most of the characters we'll be recruiting have shades of previous standard jobs, but almost always with a twist.
Terra's job is given as "Magitek Elite". This is functionally "red mage"... sort of. Her special ability until further notice is the ability to use magic, with a fondness for fire-elemental spells. But there's no clear-cut line to say she gets "offensive" or "defensive" magic, because without further interference she'll learn Cura, Raise, Arise, and Teleport -- along with Firaga, Holy, Break, Flare, and Ultima. Her equipment isn't particularly mage-like, either: she can equip robes and flails, or go for heavy armor and knightswords.
Locke's job is given as "Adventurer". This is functionally "thief" (although he'd be offended to hear it)... sort of. He's got the Steal ability, the speed, and the fondness for knives and boomerangs... but like Terra, can equip heavy armor and knightswords.
Edgar's job is "Machinist". This is functionally... um... ah... hmm. Edgar's skills don't really have an analogue to the established job system, because there's not a job where you buy your damage- and status-dealing skills in a shop and deploy them without MP cost or other penalty. His go-to skill for now is summoner-esque, with attacks that damage, confuse, or poison the entire enemy party, but later he supplements it with single-target attacks and the ability to inflict elemental weaknesses on foes.
Given his speed and vitality scores, Edgar is functionally the
opposite of a summoner, and his equipment preference is for spears, shields, and heavy armor.
As MetalSlime alluded, and despite the lack of anything in the game indicating this might be the case, the chests in this cave have some crappy gear now. If you wait until the next time you're obligated to travel through this dungeon, they're better. So I skip them.
It's not a long cave and doesn't have a boss.