Your shipping bin could hold 99 quantities of each shippable goods. Your goods will go bad in two weeks if not shipped. When you get the Frozen Ice in the Mountain cave, then you could ask to build a non- spoiled shipping bin. The person who makes the non-sploiled bin, he is in the tool shop at the Mall area.
To ship make sure you have your shippable items in the shipping bin house. Do not press any items you want to ship. Then go to your house, and use your phone before 6pm. Then pick yes, and the top choice, and you select the things you want to ship, and how much you want to ship. (Quantity, of one good.) You will have to do this over and over to ship more stuff.