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.
I made a template by scribing two adjoining squares on a piece of MDF, using compass and straightedge, then marking each corner with a centerpunch, then drilling the points with a 1/16" bit. I find I'm always breaking small bits, so I picked up a couple of each size some months ago, and on looking I found I had three 1/16" bits, which worked fine for what I intended.