The box material is just another engineering choice. Wood, ply or MDF can all be made to work, they each have strengths and weakness. Carbon fiber and steel can also work on speakers and have advantages and drawbacks. If you were commercial mfg you would use MDF for the low cost and stability of raw MDF stock in your warehouse. If you are novice woodworker you don't have planer, edger, enough clamps or glue/fastener knowledge to use real wood safely. BB is a good choice, but it is very resonant, with high Q, so bracing and damping strategies become critical at midrange freqs with BB. MDF has low Q resonance, but a wide resonant bandwidth that can destroy midrange tone quality, but simple bracing or damping can easily tame that. BB usually makes a brighter sound that people tend to like as long as enough bracing to keep it from ringing. For natural wood, spruce and plain old white pine 1x shelving wood from homedepot can sound incredibly good.