You can totally make puzzles with acrylic - I don’t know if you can sublimate on it though.
You can totally sublimate on plywood, and the light plywood that 
sells is layered wood, rather than an MDF core between layers of wood veneer. There are other sellers that have all-wood plywood, but I haven’t gotten any so I can’t speak to specifics.
One of the other things that the Spark/Aura machine is fabulous at is paper craft. Layered designs, and cards, and, and, and 
You’re going to have so much fun!