Is there a way to store purchase if I don't have an open spot to place it?

You do not need any open spots. Storage is unlimited, so it will accommodate anything you want to store. Only thing you cannot store are the coin-producing structures and island landmarks.

I'm pretty sure you cannot purchase a decoration and send it directly to the ship for storage.. it has to land on the island first and complete the waiting period for the decoration to mature. If you are completely out of space on the island you can put a previously purchased item in storage to make room for the item you wish to purchase.