The 16 gauge steel sheet is great for a sturdy faceplate, but I
usually use 18 gauge brass or nickel, which are easier to saw and
cut, for silhouette/matrix dies.
Masonite might be okay, but plywood is definitely too squishy. These
materials sound like they were meant for a die that was to be
hammered into, rather than pressed.
Acrylic is the material that is typically used, being relatively
inexpensive and easily available. However, other materials are
possible, if they satisfy the requirements of being sturdy,
un-squishable, and difficult to shatter. Other plastics, such as
polycarbonate, are great. Some people use whatever they find in the
scrap bin at the plastics store they live near.
An interesting thing to note is that it is generally easier to cut
two 1/4" thick pieces of material, rather than one 1/2" thick piece.
To hold all the parts together in alignment, I like to drill them
with with a #52 or 53 bit, and pin or rivet them together with 14
gauge brass wire.
I hope this is helpful.