There is a few money making fish, but don't expect them to sell 1 million gil per fish! Leve fish, Titanic Sawfish, the crafted item for relic has two that requires fish, and Emperor Fish comes to mind for the moment that you can sell for decent profit. (Time to get those is a different thing!) There's a few titles "Master Caster" and "of Dragon's Deep" that comes with an achievement and a quest completion. The first one comes with Ironworks Fishing Rod.

If you stand on a spot for the highest possible fish you can fish up instead of running after leves, you'll most likely get fisher to 50 in no time at all because exp per fish is pretty insane. Especially if you catch HQ. And remember to eat food, that +3% bonus exp will give you a lot in the long run and the grand company exp boost for gathering. If you need to visit down, you could turn in the Provision mission daily.