Hey JMac, let me answer as I know more about the wood available here in Germany:
Steve uses a lot of birch ply (Birke Multiplex). You can get it at your favorite home store - just check to get a good piece of wood. Also check the box with the cutting rest - sometimes a good deal.
I also like to use beech ply (Buche Multiplex). Cuts nicer, and is much better to finish. Also looks a more worthy(*). Try it!
Other woods:
- 3/4" beech (18mm Buche) is ideal for puzzles.
- 3/4" acacia (18mm Akazie) is available at OBI. It's colored dark, near walnut (dunkel braun wie Nussbaum). Don't argue - the color comes of with a light bit of sanding. Underneath is structured wood with lots of grain - comes out beautiful with some oil.
Another good source for wood is
www.designholz.com - I ordered walnut (Nu?baum) and some other woods from them. Check to order their veneer set (Funier-Set). It's a nice assortment of veneer, you can use it for bookmarks or glue them up to get thicker pieces of "custom plywood".
*) IKEA is pretty common in Germany and all around Europe. They use a lot of birch - I feel like people are a bit feed up by this.
