A flat soap surface allows for even, consistent images. The deeper the impression, the more soap is displaced, which can warp the outer edges of the bar. Smaller bars can be stamped to a lesser depth to avoid warping or breakage. Depending upon the formulation of your soap, the soap may be ready for stamping as soon as it's un-molded. Stamped designs show up best on colored bars.
White soap reflects light, resulting in less contrast between shadow and light in the image.
One way to create contrast in a white bar is to dip the stamp in dye, following the instructions given two paragraphs below. Milky Way soap stamps work in cold-process as well as melt and pour soaps. Melt and pour soap base tends to be firmer and more brittle than cold-process soap, and the stamps may consequently require an extra tap or two to register a satisfactory image. The stamped images in this softer soap display a smoother, more polished finish. After stamping, age the bars a few days to allow for evaporation of excess water.