You may want to use PVC boards, such as Azek instead of wood for less maintenance. They have the density of wood, look pretty much like wood and can be sawed, sanded, painted etc. Azek boards come as sheets like plywood or planks like boards in various thinknesses. (Note: Azek is not just house trim.) You could combine with vinyl lattice and composite specialty boards to make a nice planting box.

See this link for ideas of commercial ones you could copy:
http://forums2.gardenweb.com/forums/load/contain/msg0211131923477.html?14

Looking at existing ones to buy may be you could get an idea of dimensions when building your own.

Here is a link that might be useful: Azek Product Info

Just as followup - Azek even has beadboard! Nice. Have to convince my hubby to build a planter. Be sure to look at all the tabs under the web site.

How I know of this product is that we replaced our peeling house trim with this several years ago. This was after scraping, painting every 3-4 years. Looks nice and you can't tell it isn't wood. My painter loves it! They have much more selection of products now than when we used the product.

I use plywood for planters of various depths. My wildflower planters which hold perennials are only 12" deep. Other planters, those that support morning glory vines, I go up to 18" deep. I can't comment on growing trees. When I use plywood I paint the interior and exterior with a good Porch and Floor oil based paint that has polyurethane. This stuff covers in one coat and really protects the wood. I found Home Depot to be the best source of this paint. Some of my plywood planters are on their 4th year this summer with no visible wear. You can get the Porch and Floor paint in some nice colors but if you want something specific for the outside you can put on a second coat using exterior latex or whatever.

The insulation sounds interesting. One of the big problems with containers here in the colder climates is that they freeze up killing some tender perennials. I hadn't thought of building the insulation right into the container.