And I don't think I would even consider sinking any screw into the edge of the 1/2" MDF mentioned.
I've had great success using regular drywall screws in mdf by drilling a pilot hole, sinking the screw, then withdrawing it and dripping a couple drops of thin CA glue into the hole and quickly resinking the screw. If you wait a second or two after the screw hits bottom, then break it loose by giving it a partial turn in the outward direction, the CA makes some pretty good re-useable threads in the holes for removing and replacing screws in situations where that might be warranted.