I prefer 3/4" cabinet grade birch plywood over MDF. Dont use particleboard.
MDF is cheaper and easier to put a finish on but its also harder to work with and not as durable.
you could use car woofers, but you'll need to know exactly what woofer it is you want to use, along with all the other drivers before anyone can tell you what the box specs should be.
It would probably be better to build a passive crossover vs buy one off the shelf thats made to be sort of "one size fits all"