Fishing Quests
There are simply too many fishing-related quests in the game to provide useful details here. Instead, I recommend you take a look at this List of Fishing Quests to see which ones are appropriate for your skill level and faction.

Achievement-related Quests
On your way to getting your Salty title you will need to complete the daily quests that comprise the Old Man Barlowned achievement. These quests are offered by Old Man Barlo, standing at 38, 12 in the Terrokar Forest. That is on the shore of Silmyr Lake, just outside Shattrath City.