Hi Dave,
For framed fretwork, I usually use either fabric, felt or foamies. Most any glue will work just place some dots of glue in larger areas and apply the backing. For unframed fretwork, I use 1/4" ply and either paint or stain. Wood glue works fine but works better to lay flat and apply some weight till the glue sets. In either case, use the glue sparingly as it doesn't take much and that way no cleanup.