I use BB plywood (Baltic Birch) for fret and portrait patterns a lot. Thin, small pieces don't seem to break off as bad as with other plywood.
For crosses, word art, etc I use Cherry, Walnut, Black Walnut, Maple, Mahogany, Birch and Pine.
Some people don't like the white pine you can find in the big box stores. I have had very good success with it and it is inexpensive.
When I design a new pattern I sometimes test cut in Pine just to make sure there are no problems with the pattern.
