An aquatic base in Don't Starve: Shipwrecked can have a numerous number of benefits for any player who wants to stay alive. With the addition of many structures and items in the Home Sea Home update, an aquatic base is both a possibility and amazing.
The first thing to do is to find a location. A good place to choose is a coral reef, as you can get easy access to coral and the Bottlenose Ballphins can be hired for help with sea combat. If you are playing as Webber, Ballphins will be hostile, so try to find a coral reef without any Ballphin Palaces. The reef where the Yaarctopus makes its home is also a good choice.
The first thing to put in an aquatic base is a Sea Lab. This is equivalent to an Alchemy Engine, and can only be placed in water. Once you have placed the Sea Lab, it can serve as a crafting station for all of the other structures and items required for the base.
The next thing you will need is a tar extractor. Search the waters around your base for tar slicks, and use tar extractors to collect the precious fuel. The tar will be needed for the next item in your base, so be sure to collect enough of it.
The next thing to equip your aquatic base with is a Buoyant Chiminea. While boats can be equipped with boat torches, boat lanterns, and tar lamps, a Buoyant Chiminea is not affected by strong winds, and can be used to cook food. A Buoyant Chiminea provides enough light to keep Charlie away.
With some leftover tar, craft some Sea Chests. These are cheap to craft, and are your only source of storage at sea, aside from Packim Baggins.
Fish farms can be used as a reliable source of food while at sea. Spider Dens are a common sight in Jungle biomes, and the silk can be obtained easily. Killing multiple spiders to make multiple fish farms is recommended, as the silk is a relatively common drop.
The third structure for your Sea Base that requires tar is a Sea Yard. Although the resources used to make it can be expensive, it is a way to repair your boat that does not require the murder of innocent bees, and once placed, all of the ingredients required to fix your boat can be found at sea. It is recommended to have your sound on whilst repairing your boat so you can tell when your boat is fully repaired.
By the time you are even considering making a water base, you will have at least a row boat, if not a cargo boat, armoured boat, or the 'Sea Legs'. However, your boat's durability can rapidly decrease if using it to travel the short distances around your base, from your Sea Lab to your Tar Extractor to your Sea Yard, and so on. Make a raft and keep it at your base for the sole purpose of moving around your base.
The final thing you will need for an aquatic base is sea walls. Requiring only limestone and seaweed to craft, sea walls can keep basic threats at bay and also make your base look cool. Although not a requirement, these walls add a nice aesthetic to your base and can separate different parts of your base.