Ships:
1. There should be a separate line of 'Pirate/Barbarian' ships: no pirate ever built or sailed in a Battleship, which is what a Quadireme represents in its Era, and very few even had ships as big as a Frigate. Suggested Barbarian Naval Line:
Barbarian Galley - available at Start, melee unit, Move 4, Melee Factor slightly less than a 'regular' Galley BUT can Pillage coastal Improvements and raid cities for Population Points - the most dangerous form of early piracy was not taking ships, but raiding coastal towns and villages for loot and slaves.
Barbarian Xebec - available in Medieval Era, melee unit, Pillage ability as above.
Barbarian Brig - available in late Renaissance, melee unit, can only be seen if adjacent. Pillage ability as above. Usually, the best way to get rid of Pirates was to destroy their bases.
Barbarian Gunboat - available in Atomic Era. Can only be seen if adjacent. - the 'modern' pirates, in small boats that terrorize shipping, but are totally unable to fight warships if caught. Could also be given a 'Smuggling' option that reduces Production, Amenity, Loyalty, etc.
2. Regular Ships.
The Caravel was a very small-hulled ship, which couldn't even carry any decent-sized artillery. It makes a lousy combat unit, to be blunt.
The options are:
Medieval:
Cog - combat ability was in the temporary - later permanent - 'castles' at bow and stern, which could be filled with archers, crossbowmen, and men-at-arms to outshoot, board and take an enemy. Rather than a separate unit, since almost all the hulls were just converted merchantmen, I'd make this a new Ability for medieval units: when they embark, they can attack other ships using a percentage of their melee/ranged factors.
Medieval/Renaissance:
Carrack - the first 'big hull' ship, starting in the early 15th century carrying small cannon, by the late 15th century carrying 'big guns' . The first possible, then, Ranged Combat warship after the Classical Era and first Ranged Combat ocean-going ship.
Galleon - if not a Spanish Unique, was first ship hull-type designed from the start to carry cannon, starting in mid-16th century: at about the same time as the Galleass, in fact.
By the end of the 16th century the race-build Galleon, without the towering sterncastles of earlier designs, was the 'prototype' for the Ship-of-the-Line: it could carry more and heavier guns, sail faster, sail closer to the wind, than any previous gun-armed ship.
Flota Galleon - this should be the Spanish Unique ship, if one is needed: standardized for the Treasure Fleets in 1613 - 1618 CE, race-built well-armed merchant galleons that carried some of the most fabulous cargos in history.
Ship-of-the-Line - a development of the race-built galleon hull in the mid-17th century that became the Standard Battleship until armor made them obsolete.
In Game Terms:
Medieval:
Cog - attack ability for embarked units, with either their ranged or melee factor
Renaissance:
Caravel - melee, low factor, high speed and vision, primarily a scouting/exploration vessel
Galleon - ranged, relatively high melee defense factor
Industrial (early)
Frigate - melee, high speed and vision 0- after all, they were used as scouts for Battle Fleets
Ship-of-the-Line - ranged, very expensive to build and maintain, but can blast poorly defended cities to bits.
Both the Frigate and the SoL can be Upgraded with Steam to Steam Frigates or Steam Battleships - added steam engines, shell-firing guns. Still horribly vulnerable to Ironclads, but it can extend your 'Ship-of-the-Line' investment for another half an Era or so.
Industrial (late)
Cruiser - melee, high speed, vision
Ironclad - ranged, requires lots of Coal to maintain
Modern:
The usual suspects: Battleship, Aircraft Carrier, Destroyer, Submarine, etc
I DO NOT believe the game necessarily needs all of the above, but for the Naval Masochists who want to be building, upgrading, rebuilding ships every 40 turns or so, there they are . . .