I usually go with 3/4" MDF, some 1.5" wood screws, and pleanty of liquid nails. Assuming you're using butt joints, you'll want to pre-drill and countersink all of the screwholes while using liquid nails for all of the joints.
You might also consider sealing the inside of the box with a resin. At the very least, you'll want to goop all of the inside corners. You might need some internal bracing for your brahma and buttloads of power too.
