I'm currently in the early stages of working out the likely might, wealth, and influence of a small duchy for plotting purposes in my fantasy (14th/15th century-ish tech) story. Here are some key notes you might need in order to better answer the thread's question. (1) The total population of the duchy is just under 40k (2) It's located on an island roughly the size of Jamaica (3) The reigning duchess is considerably wealthy, as she owns numerous profitable enterprises, the largest of which is a shipping company that operates in something comparable to the Mediterranean Sea (4) the duchy's primary military obligation to its monarch (who resides on the same island) has been, and continues to be, naval support My questions to you are: how many warships might the duchess currently have? How many cargo ships might her trading company have? If you need more information I'll provide you with what I can. But keep in mind, this story is just coming out of my early brainstorm phase.
The Battle of Curzola (which occured in a time frame comparable to your setting), saw the navies of Genoa and Venice almost entirely destroy each other. Genoa had 66-75 galleys at this battle, while Venice had 95. Genoa's specific figures aren't known, but Venice lost 83 ships. Working off of these figures, I think somewhere around 20 warships is reasonable. Finding figures for merchant ships is harder, but giving the duchess a similar number to the warships would give the impression of considerable wealth you're going for. Population might mess with those numbers, though. How many of those 40k make their living on the sea?
That's really solid info @X Equestris. Thanks. The majority of them, as seafaring is the best path to earn a decent living inside the duchy. I imagine the labor force breaks down as sailors>farmers>merchants and tradesfolk>full time soldiers for the duchess>hunters & trappers>and other.
In that case, I think the 20 warships, 20 merchantmen figure works. The Wikipedia page on Curzola puts Venetian losses from those 83 galleys at about 7,000 dead and 7,000 captured. 14,000 total. Divide by 2 (for the Duchess's 40 ships) gives us 7,000 as a rough estimate of the sailors, marines, and civilian crewmen between the two fleets. That's a big fraction of the duchy's total population, but not inconceivable. Especially if most of the navy isn't a standing one.
With those figures in mind, I think I'll put them at 18 warships and 19 merchant ships, so I can untie a little more of the population from the sea. That's more ships then I imagined anyway. In regards to ship types—and admittedly I haven't researched them much at this stage—I was thinking of a mix of cogs and caravels. Does that sound right? The culture I'm shooting for will have a mix of influences from Sicily, Spain, and possibly even Carthage in its heyday, if you can imagine that.
You mentioned the shipping company, at least, operating in a Mediterranean equivalent, so I'd go for mostly galleys, dromons, and coccas. That last one doesn't come up very often in fiction, but it's basically the Italian equivalent of a cog. Maybe throw in a caravel or two. You might even bring in a galleass as a naval flag ship, though those are pushing the upper end of your time frame. The exact composition of things will probably depend on the waters around this island. Calm, Mediterranean-esque waters lend themselves to oared vessels. More violent, Atlantic type areas need ships like cogs, hulks, and caravels.