A good time to begin base building is a little earlier than midway through calm season. By this time you will have explored a bit of the map and will have several islands to choose from. The type of island you are looking to settle on is one that has both jungle and beach biomes as this will provide the most in movable resources (saplings, grass, roots, bamboo) and immovable resources (limpet rocks and seaweed).
Make sure you don't build any of your structures or objects near the ocean line as they will eventually be flooded during hurricane season and those resources will be wasted. A better option than the standard Firepit is to build a Chiminea (2x Limestone, 2x Sand, 2x Logs) before the hurricane season starts as this won't get flooded or blown out by strong winds. Lightning also strikes constantly during hurricane season so consider building a Lightning Rod using a Science Machine (costs 3x Gold Nuggets and 1x Cut Stone to craft) to prevent out of control fires and provide more light.