Family businesses often owned ships and often the captain was an employee of the business, a trusted professional but not part of the family. Other times, the captain with a successful track record would acquire a ship by forming a venture pool and being a part owner.
My impression is that sail-only vessels were still doing trade through the 1920s but declining. Hell, a lot of local commerce on the broad waters of the Tagos is served by sail even today.
I doubt you would find a "passenger ship" in the sense of a liner under full sail, although I could be mistaken. It was cargo, and the passengers came along. Sailing vessels did not carry that many passengers, cabin space being an afterthought to the main job of moving cargo. The Euterpe, a wool clipper, carried plenty of emigrants from England to New Zealand, but always made her big money bringing wool back to the mills of England from New Zealand.
Captaincy was earned by saltwater time and experience. Keep in mind that in the hands of this single man the entire vessel and her fortunes were entrusted. The whole venture rode on his judgement especially in bad weather or tricky straits. A captain in his forties was (I would guess) lucky to get a ship so young. These are just impressions, though.