Before you even start thinking of going out and exploring you should consider completing all the quests on the starter island. The starter island is basically a tutorial which is easy to do and will introduce you to the basics of the game as well as giving you a decent set-up to start with that includes a house, workbench, and a good set of starting materials.
Completing the tutorial is essential if you are new to the game as it teaches you the basics of fighting and also explains the importance of resource gathering and activating the portals in each world. Even when you have opened your first portal its worth staying on the first island until you have seen everything that it has to teach you.