In that Tansu were intended to be functional rather then decorative, design can be generally ascribed into two chronologic periods: EDO (1603 - 1868) and the early IMPERIAL RESTORATION (1868 - 1926).
Because the Edo period was feudal in its socio-economic structure, rules concerning ownership dominated all classes from peasant to Samurai. Traveling was tightly regulated and conspicuous consumption discouraged (chapter 1 of TANSU, pages 23-56 speaks to this time specifically with photos of representative cabinetry).
With the coming of the Meiji Restoration in 1868, "the occupational specialization of the Tansu maker eventually became discernible from those of the box maker and the joiner .... because of disintegration of the rigid class structure and the development of distinctive regional characteristics" (from TANSU page 32) For a detailed overview of the range of designs that flowered during the Meiji Period, please refer to chapter 3 of TANSU, pages 100-161.
Not unlike America's Shaker craftsmen, Tansu artisans shied away from using woods that were not indigenous to Japan. Because chests were often set into alcove spaces as an architectural addition, exposed face wood was of superior quality, especially after 1868.
Tansu finishes fall into two categories: dry and lacquered. For a dry finish, clay or chalk powder was rubbed into the soft wood surface (Paulownia, Cedar or Cypress), then burnished with a reed whisk. For lacquer (Rhus Verniciflua), application could be for simply sealing of the the plain wood to enhance a natural visible grain or for the creation of a perfect opaque surface of great value. In that the uses of lacquer might best be considered in detail, I invite you to refer to chapter 8 of TANSU, pages 219-230.