3/16" Masonite, Lowe's is the place to get it cheap. Is it archival, no. Does it work, yes. It will yellow over time, but prime the crap out of it, and you'll be fine. Backed with 3/4" MDF.
Glue is your friend. The MDF will guzzle the glue, so use plenty.
3/4" MDF ripped to your preference, the smaller the size, the more risk of bad results. The MDF is a cheap, and will split very easily. This cut was not made free hand, that would be bad. Be safe with a table saw.
So, you have a masonite top, nailed to a basic box frame on the back. Glue is your friend in this step.
The MDF gets drunk on glue, so make sure it gets plenty. Also, make sure you have beer in the shop fridge, you deserve one at this point.
4" x 5" Panels
8" x 10" Panels
Now all you need to do is puddy some flaws, give it a little sanding, prime it, and off to production. Whether a Scott Krichau character study, or an Original "Wenchkin" Painting, these panels are awesome.
Update 2-11-2012
Carolyn is sanding all the edges of the panels. The reason one should break the edge is to make the panel more stable. This task is super boring and taxing, but important. It helps keep the MDF from chipping and ruining the panel. The sanding helps ensure the longevity of the panel.
Priming to come this afternoon, pics when the next step happens