Shipping can be done in several ways. Traders can move goods from one port to the next for their own profit. Shipping companies are in the business of moving goods for other businesses at a fee and the cargo they move is insured. A strong shipping business is essential to a port and the local government and the Navy will do their best to protect it.
Every port in Rulers of the Sea will have its own culture and occupants, making it infinitely interesting to explore them, do business in them, and maybe even making them your home and help to develop them.
The family business can be a real purpose for a family, or just a side-line next to other careers, but either way they are an interesting method to earn a good family income, if managed well.