Ryan> The major goal of any cabinet is to be free of resonance. It has to be "dead" or the cabinet will color the sound. Think of it like a guitar body, a flimsy speaker cabinet works the same way. Typically, you don't want to use solid woods or normal plywood because they will ring or in the case of plywood it can have voids inside. Not to mention there can be little scraps in the voids that will rattle. Baltic Birch plywood that is void free is an exception.
Thinner material, unless it is very well braced will let the panels flex as the speaker plays. Again, very bad for sound. Bottom line is, you can't make a box too solid, but deffinately you can make one too light. MDF is a fine choice for cabinets, it is inexpensive, very dense and easy to machine. The only consideration is finish. Hope this helps.
The goal of a cab is to have it's resonant frequency either higher or lower than the passband where the driver is operating. That can be done with a heavy high mass cab, or a lighter very ridged one. Neither design should have wall vibration.