I like most of this, but as you're fond of pointing out, this is a game. So there needs to be a balance. Perhaps as suggested, while the admiralty issues the ship, we can fudge a little reality and choose from a list.
Also, I would point that captains did make money selling and capturing ships. Prize money was how captains and crews really made money, their salaries were rather pitiful. They wouldn't get the FULL amount, obviously, but they'd get a percentage based on their rank. That would allow them to spend money on things like replaceable upgrades (extra gunnery training, say, because the Captain could afford extra powder to train with).