What are the maximum levels for the different ship types?

Below are the maximum levels for each of the capturable ship types. The easiest way of bulking up your fleet is with Frigates and Man O' Wars, but having 1 or 2 Schooners and Brigs is beneficial too (because of their speed).

Best way of farming Frigates and Man O' Wars is to get maximum wanted level and then fast travelling to different naval areas. When doing so, within a minute or less of leaving dock, you will encounter both a Frigate and Man O' War. Try engaging them separately as they can still deal a fair bit of damage even when your ship is fully upgraded.

Schooner
Level 11 – South Caribbean

• Fire Power: 15
• Speed: 70
• Cargo Capacity: 20
• HP: 27

Brig
Level 25 – Chinchorro and Charlotte Zones

• Fire Power: 25
• Speed: 60
• Cargo Capacity: 35
• HP: 50

Frigate
Level 38 – Chinchorro Zones, At Maximum Wanted Level

• Fire Power: 35
• Speed: 50
• Cargo Capacity: 50
• HP: 70

Man O’ War
Level 60 – New Bone, At Maximum Wanted Level

• Fire Power: 70
• Speed: 30
• Cargo Capacity: 90
• HP: 150

The rest of the ship types and levels can be seen in this article. I'm not 100% sure on the levels of Gun Boats, but as you cannot capture them and how brittle they are, I don't think it matters all that much.