I’ve made several puzzles trying different methods and materials. You can use ¼” plywood with no voids, or ¼” masonite. If you use plywood, before you start cutting you should coat the back side (good side) with some sort of finish to prevent warping and splinters. When you do get done cutting, there will be a little bit of sanding necessary on some of the back edges. Because of this I prefer using masonite since no sealing or sanding is necessary.
To glue the picture to the wood you can use white glue, spreading it smooth on the board. Spray adhesive also works just as well. Using an old credit card, use light pressure to work out air bubbles. Don’t scrape the picture with the edge of the card or it will scratch the picture. Also it is best to get the “matte” or “lustre” finish to minimize scratch marks. If you get glue on the credit card, wipe the glue off before touching the picture again or you may ruin the picture. Plan on cutting at least ½” off the picture after gluing, because it is difficult to smooth out the picture all the way to the edge.
When making a puzzle for a child, if you’re not going to make all ear and socket interlocking joints, it helps to have a border to keep the puzzle pieces from moving around while putting the puzzle together.
One way to do this is to tape the puzzle board on top of the border board using double sided tape. Cut both of them together when cutting the outside border.
Before doing this however, you’ll need to drill a “starter hole” in the border board where the hole will be inside the puzzles’ edge. In other words, drill the hole in the waste part of the border board. This is so you can drop the scroll saw blade through to start cutting.