You actaully can get linen to press wrinkle free, the key is to iron it while it is slightly but evenly damp.
They can all play together well if they are pre-shrunk, and are of similiar weight. I personally would not make shorts out of any fabric with a high linen content. The wrinkles, as the garment is worn in this case specifically in the groin area, are not very becoming/flattering.