Any outdoor architectural elements should be made out of wood species that are resistant to rot. This almost always means a softwood, because softwoods contain more pitch and sap than hardwoods and last longer in wet conditions. Cedar is one of the most rot-resistant woods available. This quality, combined with its light weight and workability, makes it ideal for items such as shutters that will be exposed to all kinds of weather and will be suspended by hinges or screws on the outside of the house.
Even rot-resistant woods should be treated and protected to maximize their lives. Cedar can be protected with clear polyurethane or various types of water seal to maintain the beauty of its natural grain, or it can be painted. You will need to prime cedar before you apply a finish coat to help the paint adhere to the wood. Paint all surfaces of the shutter, including both sides of the louvers, to prevent water from gaining access to the wood and beginning the rotting process.
Any cedar that is used for building shutters should be either kiln dried or air dried for at least a year. If you build shutters with green cedar, they will almost certainly warp and present other problems, such as splitting, as they dry. When you buy lumber, ask the salesperson how it was dried. Dry cedar is very lightweight and easy to work with. When cutting parts for a shutter from a board, avoid including any knots, as these will introduce weakness into the shutter.
Cedar is more expensive than other softwoods, but for durability and resistance to decay, it is worth the cost. You can also build shutters from pine or spruce, and they will be satisfactory, particularly if they are well painted and don't get wet all that often. Both pine and spruce can be bought at lower prices than cedar.