Welcome to the forums!
Regarding your question...
Whether you go workboat-first or worker-first on a start is going to depend, but generally getting workboats to hook up your seafood resources should be one of your highest priorities (spending 30 hammers to start getting 2-3

per turn extra is an extremely good deal). You may even build a workboat a bit in advance in one city so that it shows up at the new site the same turn as the settler makes the new city, and you can work a new seafood tile there immediately.
On maps where AIs are likely to be on accessible islands (e.g., Archipelago), one or at most two early workboats for scouting and contacting them is useful.
If you have seafood tiles to protect and a lot of coast (or nearby islands) so you can't just spread cultural borders everywhere to stop them from spawning, you'll probably want a galley to defend against barb galleys at some point. When you get this galley varies depending on map and difficulty level; get a galley before you get your fourth city would be my very rough estimate of typical time to do so. As you expand, you may want another galley/trireme or two to defend.
Get galleys as needed to escort settlers to new islands on water-heavy maps; you may end up with 2-3 this way. Often your barb-defense galley(s) can do double-duty helping with this.
Two caravels when you get Optics can be nice. One heads east, the other west. Both hopefully contact other civs, and ideally they get you the circumnavigation bonus of +1 movement.
Beyond that... you get the navy you need. In single-player, naval warfare generally isn't worthwhile before Astronomy and Steel (so you only get navy as you need troop-transport capacity). After that, it's going to depend completely on the game.