Tome of Heroes has a two or three page "trading company" rule set for down time. It assumes the players can find a trustworthy captain/manager and are involved just a few days a month.
An older, but more complex system is in the Expedtious Retreat product "The Silk Road". It was for 3e but that really doesn't matter much.
As for making it a ship-based game, you have options. Privateer is a fancy word for "sanctioned piracy", or they could be knighted or whatever and told to hunt pirates.
Alternately, places in distress often need food. Have them carry a shipment of grain to an area suffering a poor harvest, except the players hear rumors in the dock bars that the harvest is actually cursed by a witch and boom, adventure.
They leave there with a hold of Whatsits ( whatever the town might have to sell) that they got at a low price being heroes and all. They can sell it at BigTown for a modest, reliable profit or go to Backwoods, which is always trying to get a merchant to bring them more Whatsits but they are out of the way and too small for a big ship.
Either way, boom, adventure!