Hey Tony, If you are talking about stand up puzzles, just about any wood will do. If I am going to paint it, I use pine - just because it is cheap, but poplar, walnut, birch, maple, red oak all work well. I stay away from woods that burn easily like purple heart. Again, if it is a stand up puzzle, I use 3/4" wood because it is readilly available.
I use mostly #3 and #5 reverse tooth blades for these types of puzzles. The smaller blades tend to flex on your turns and prevent a nice fit. I bounce between Flying Dutchman and Olson blades. Both work well. Usually the amount of detail determines which blade I use. (I lean toward the #3). The Flying Dutchman puzzle blades work well on really thin puzzles but wander too much for thicker woods.
Good luck with your project.