Here is what I was thinking....

You will make a frame out of 2x4s, you have two options to make it look
better than just slapping it toghether....

Option 1
A standard 2x4 is sanded on all 4 sides. This creates rounded edges. If
your 2x4 is visible, you will have a gap where it meets the edge of the
plywood. Find somone with a long bed jointer or a planer who can trim
the 2x4s to make them perfectly flat or square. Once attached, it will
look better, because it will fit tighter and have no gap at the edge of
the 2x4 and the plywood. You still have the issue of the ugly edge of
plywood which will still be visible after painting.

Option 2.
make your 2x4 frame, do not worry about planing or jointing the 2x4s
unless its easy to have this done and doesn't cost you anything. you
will then wrap your 2x4 edge with the plywood. This would require you
to cut a very accurate 45deg edge on the surface plywood and on the
front plywood edge. Attache these with glue and screws to the 2x4
frame. Upside of this aproach - it will look the best. Downside of this
- It will be very dificult to do if you do not have a perfectly
straight frame and acurate cuts on the plywood.

Good luck