Buying and selling
At the shop you can buy and sell everything your crew needs to be strong and healthy. For the most part you just want to buy food and water, and maybe sell of some barter goods. There are some goods that have no use but trading.
The market is a bit different... here you will get an offer, that is almost always cheaper than the shop. But you cannot control how much of it you want, and if you cannot afford it; it will be a deal breaker. It's a good idea to visit sometimes, buy some barter goods and sell it of at the store the moment after.
Food and water
You and your crew will need both food and water for traveling at sea. A half carton of food and a whole barrel of water for every crew member, including yourself, per week. You and your crew won't die however, but they will refuse to travel any longer. When this happens, you need to land your ship at the closest harbor and buy more at the shop.
Tobacco and rum
You won't need these, but it can come handy. Tobacco will raise your crew mood by 1 and rum will raise it by 3. You can give your crew these products by clicking in the inventory, choose which users to please, and choose which product to use, and click "Do it!".
The same way you can give your crew members tobacco and rum, you can also give them medicine. This will restore their health to 100 % and it can be used everywhere. There is a healer at the market, who is cheaper than using medicine, but you aren't always at a town. Besides, you will loot medicine from enemy ships anyway.
This includes porcelain, spices and silk. You don't have any use of these goods, but you will loot a lot of these at sea. You can them sell them at the shop and make money that way.