there is nothing wrong with plywood. it all depends on the quality that you get. if you get the super cheap crap, well ya, itll be a problem. you could get 1/2" apple ply and that would be stronger and much lighter than 3/4" birch or mdf but itll cost you about $100 a sheet. when looking at plywood, the more layers the better. mdf is used because of its density. it wont vibrate as much as a lighter wood.
when people glass the inside of the box they just use the resin, no mat. the reason is because wood breaths and the resin seals all the little microscopic holes. its good to do on any box but it will change the sound a little. just like each type of wood will have its own sound.
so its all up to you on the amount you want to spend on wood.