This is what has always worked for me:
The base material depends largely on how I want to show off a model. For most figues I use the basswood plaques, becuase the machined edge dresses up the presentation. For dioramas, I use plywood, or MDF. After determining the height of the groundwork, I cover the egdes with aircraft plywood or hardwood strips, both of which take a stain or varnish well.
For built up groundwork I used the kind of dense styrofoam used for flower arranging. It's green, and can be found in most larger craft stores. It cuts with a hot wire, jeweler's saw, or even a craft knife in smaller pieces. It doesnt crumble (although as someone else said crumbling might be a useful effect). To fasten it to a base I use a contact cement.
It's not a good idea to just apply Celluclay or other papier-mache based groundwork materials directly to plywood, even if it's sealed. It may be I have been unlucky, but I have never found a sealer which can stand up to several days of being under Celluclay while it dries. The boards always warped! I would recommend you use styrofoam under it first. Another alternative I have had some sucess with is using Woodland Scenics plaster gauze. Celluclay shrinks over time, I have discovered; imagine the surprize of large cracks appearing under the feet of the figures on a base (we're talking foot-wide cracks in scale, guys... OK if the diorama is depicting an earthquake, I guess). The hydrocal plaster in the plaster gauze doesn't shrink.
Ne cede malis (Latin: Yield not to misfortune)