Which material sounds better for speakers construction? Wood, Ply or MDF?

There is no absolute.  
MDF is more dense than plywood or wood.  Wood on its own depending on type has all kinds of problems with expansion and contraction.  Plywood works, but still is a softer less dense material... However, if you are after an effect,  plywood can be more giving than MDF.. Also, the is no problem with gluing MDF & Plywood together, this works.  Way back when,  we built a cabinet out of concrete & ground up Styrofoam, worked great.  Also a few decades ago, I believe Definitive made some concrete enclosures.  

Anyone building DIY cabinets can use Corian at the very least:
Best materials are composite polymers. And this is not debatable.


Even though Corian would work, I want anyone to be careful that might plan a diy project,  you can't grab any material because it looks dense. 
Corian is an acrylic mineral.  As long as the cabinet is thick enough, it will do a very good job 
And I'm sorry to say that composite polymers are debatable,  They can be excellent, but It very much depends on which polymer and hardening agents are used and again, how thick the material is to absorb or repel bass frequencies from within the box. Phenolic resins or some epoxy's could work also. Some of these materials sandwiched with a softer material could be excellent. 
Its not that this is wrong info, but in itself if not used properly can end in some pretty poor results. I hope this helps. 

There are a ton of excellent speakers made of many types of materials.  In the end, as long as a cabinet is well designed with the cabinet included in the design,  the drivers and crossovers are still more important to the overall design than the cabinet material itself. 
Again, well thought out, well designed speakers that include the cabinet material in the design. 

carbon fiber makes sense to me... it is a very dense material that is dead and if bonded over another would offer a very nice damping material.  

@geoffkait     Well actually you are correct, I really should have thought through my words better... it is low density, because it is lightweight, but I guess we could compare carbon steel or you could call coal a carbon as well as diamond a carbon, but no,  I meant carbon fiber, more like an epoxy.  I thought you were part of the forum,  its called chiming in, not butting in.  So, I stand corrected, but still contend that this could be a very nice material combined with another. 
Tim 

knock on your cast aluminum engine block and tell me how it rings.