I suggest none.
The Starter Kit comes packed with components. Some of which aren't even used in the Project Book.
The reason I say none is that it's best to work your way through the book first. Build the boards, code the sketches. Understanding the code... projects. Once you have a grasp of the code and functioning of an Arduino board you can decide what components will be useful for you.
I did order another part with my starter kit. A relay switch. I wanted to learn Arduino because I need to build a thermostat for my pond heater. Now that I have the kit and am half way through the book I realised that the relay switch I got isn't suitable for my project. And that's a waste of money.