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

Good quality MDF doesn't need finishing on both sides. You can leave the inside surface bare. 

I prefer speaker cabinets made of ice if you can keep the listening room cold enough...otherwise you wind up with a wet pile of components on the floor and, seriously, nobody needs that.

When building my three way, triamplified all horn loaded DIY speakers I found a constrained layer construction of 3/4" marine plywood, 1/8" neoprene rubber and 1/4" aluminum to be a good choice for critical panels.

There are some who still feel that using MDF alone in a traditional cabinet is a tonal midrange killer. So naturally enough many other options have been explored, all usually costing far more than the readily available and cheap to work with MDF. Some cynics might argue that they were the only reasons for MDF becoming almost ubiquitous in the last 2/3 decades.

More recently composites have become increasingly popular. Peter Comeau, formerly of Heybrook, now working with IAG-owned brands like Wharfedale, Quad, Audiolab and Castle, has been studying cabinet resonances for decades, and now uses chipboard/MDF composite panels for his loudspeakers.

Harbeth stick with MDF / bitumen damping panels but their cabinets use a unique ’lossy’ construction which flies in the face of all those who favour high rigidity above all else. Harbeth also firmly believe in using veneer on both sides of the speaker panels - presumably to ensure long term stability.

Nobody yet has claimed to have been able to make those pesky cabinet resonances totally inaudible, and it’s difficult to see how they could, but the choice of where to put them will always partially depend upon what material you use to build your box.

Fans of panel or open baffle speakers will have to look for other things to worry about.

https://www.google.com/amp/s/zstereo.co.uk/2018/10/20/peter-comeau/amp/

I really enjoy my solid wood (Sapele) speakers.  Most speaker companies will not build their speakers out of solid wood because the expense would be to high.  There is a correct way to build speakers out of wood which is very time consuming. I know there is more cost to a speaker then the cabinet.  But I couldn't spend 10's of thousands of dollars on a MDF cabinet with bondo filling the gaps. As for sound goes. Everybody has a personal preference no matter what it's made out of. Find the best speaker that plays the most genres of music really well.