Here are some stats I've put together for a potential in-game 3rd rate:
Armor: 16,800
Sails: 15,000
Speed: 9
Cannons: 16 (7 on each side, with 2 facing directly forward)
Broadsides: 30
Cargo: 18
Crew: 14
Turning Radius: Very large
(Around 10-15% larger than that of a base frigate)
Weak Armor Location: Back
Strong Armor Location: Front
Base Cost: 150,000
Resale: 75,000
Required Sailing Level: Mastered
Upgrade Costs: Can be discussed later
Ships of the line are basically giant frigates (referring to real world design), so I used the war frigate's stats as a base template. When progressing from light, medium, to war, frigate armor increases each class by 4,200 and the sail health increases by 3,000. So that's how I arrived at those numbers. The broadside count is high because that it is the defining characteristic of any line ship. Without that, it might as well be a different ship. The tank and damage potential makes up for the undesirable maneuverability. Don't underestimate the drastic effect that not being able to turn quickly can have.
Possible means of acquisition:
A ship of this status should require more than just 150,000 gold and mastered sailing. So I've thought of a short quest that would need to be completed before purchase.
Title: Rite of Admiralty
Quest Giver: any shipwright
Objective: Show the shipwright that you have 1 of 4 swords in your inventory. Admiral's/Vice Admiral's Cutlass OR Admiral's/Vice Admiral's Sabre.
Simple, difficult, perfect.