What type of thin or light wood is suitable for making box joints?
Plywood is ultimately the answer. When making box joints or finger joints you need to have dimensionally uniform and preferably stable wood. 

Plywood comes in many sizes and I would imagine something like 8mm would be fine. If you are OK with something larger like 16mm then you would have stronger joints as there would be more surface area.   

This is dependent on what tools you have. A box joint jig on a table saw would make this a breeze. 


  I read here that pine wood is easy to shape and stain.


Pine is cheap. That is its main advantage. Most softwood is easy to shape by nature. Easy to stain is inaccurate as pine (and other woods) is susceptible to blotching. Blotching meaning a non-uniform stain.

Real wood will almost always certainly look better. On box joints you are going to see the plys more so you need to know if that is something you are comfortable with aesthetically.