Regardless of which type of screw you use, you'll need to flip the panel and use a countersink drill to on all of the exit holes. Drilling MDF leaves bumps, the countersink bit will remove them, and will create a little bit of space for material drawn up by the screw from the second sheet of MDF. You want to remove anything that might keep the two panels from mating up flat. I set a block plane to a very shallow bite and ran it over what was left of the bumps and over the edges. The edges of MDF can be bulged by by sawing or just by handling, and you want to knock that down.
These sorts of things are usually glued and screwed, but it's actually the glue that holds them together - the screws just hold everything tight while the glue cures. Screwing into hardboard or 1/4" ply is an exercise in futility, so I just used glue, and used my two 4x4's as long clamps. It would have been a bit easier, if I'd done this before I'd rough-cut the 4x4's, but it worked out.
We are especially proud of Post Woodworking’s Brunswick style shed. It has all the rugged features and simple, beautiful mystique of a Maine coastline. Natural-wood siding options, in pine or cedar, offer a rustic aesthetic. Or, choose a vinyl color that complements our home. Once inside the Brunswick, its unique, two-sided sloped roof maximizes headroom, making space for you to better maneuver a rake. Black architectural hinges and hardware lend distinguished contrast and quality to this basic but appealing storage solution.