Each ship serves a purpose, and while you will see some bought more than others, a good navy will buy some of each (assuming it can afford to).
All ships, except Barques, can capture “convoy zones”.
attack / defense / movement / cost
0/1/2/8 Barques are transports. They can defend (at 1), but are not good at attacking. They have “3” space, meaning that they can carry 3x marines, or 1x marine + 1x general land unit, or just 1x cavalry.
1/1/2/6 Cutters are like the artillery of the sea, but are also good fodder. They are cheap, but without units for them to support they are not very good (they support brigs, frigates, and battleships, by giving them +1 attack). Their main disadvantage, besides the fact that they need ships to support, is that they can not carry any units at all.
1/2/2/8 Brigantines are the mainstays of most fleets. They are hardy vessels, good on defense, very cost effective, and if paired one to one with a Cutter, the Brig will receive +1 attack (making it 2/2). They can also transport a single marine.
2/1/2/9 Corvettes are special attack and interception vessels. They do not receive support from Cutters, but they have other advantages: First Strike (just like submarines from Revised), and the ability to retreat separately on offense, and retreat on defense, to any adjacent friendly or empty sea zone. They can also transport a single marine.
3/2/2/12 Frigates are heavy vessels, with good bombardment ability. If paired one to one with a Cutter, the Frigate will receive +1 attack. They bombard @3, and can carry a single marine.
4/4/2/21 Battleships are the pride of every navy. They have 2 hitpoints, but do not repair. If paired one to one with a Cutter, the Battleship will receive +1 attack. They bombard @4, and can carry a single marine.
The sea units have been balanced for more than 1 year of playing.
Technically speaking, buying 3 cutters + 3 brigantines, will be better than any other buy you can think of. But there are very good reasons to buy things other than just brigs and cutters.
If you want the most offensive bang for the buck, you will buy lots of corvettes.
If you want purely defensive power, you will buy mostly brigantines.
If you want the most bombardment for your buck, you will buy lots of frigates.
If you want a well balanced navy, you will buy a good mixture, including many cutters, brigantines, and a few corvettes, and a battleships or frigate or two.
Why should you buy a battleship?
First, you don’t have much “production space”. If you move a general (the moving factory, the guy colored in red) into a territory worth only 2, then you can only produce 2 boats there. Maybe you have enough money to buy 8 brigantines and cutters, but with only 2 space and things to do, you might just need to buy that BB.
Second, do not ever underestimate 2 hit points. Even without the ability to repair, it is still huge. For example, lets say you buy 1 frigate and 1 cutter, while I buy a battleship. If the enemy deals 1 hp of damage, you lose that cutter and the value of your attack shrinks by 2 and defense shrinks by 1. I absorb that damage and keep hitting you for 4.
You will see that while cutters and brigs are the most popular, Battleships and Frigates and Corvettes are still quite popular.