There is nothing like walking into a kitchen that has the warm look of a copper back splash. Copper sheet suitable for use as a back splash comes in a collection of finishes: smooth, hammered and a estimate of unique textures are available. A copper back splash can be installed just like flashing on a roof, or you can cover a board with the copper sheet material and setup that, as you choose. Generally, when copper sheet is used as a back splash it is not nailed or screwed to the wall, instead, use an adhesive caulk that is compatible with metals. If you want to reserve the shiny look, use some thin coats of lacquer on the copper. This will help safe it from fingerprints or changing color. Leaving it natural will corollary in darkening and even some greening. This is a self-protective patina, which is valued by many because it adds character and depth to the metal. You may also clean it periodically with Twinkle (or some other copper cleaner/polisher). Keep in mind that copper is a softer metal which is branch to scratching and denting; again, this is a look that many population desire.
Copper sheet comes in a large range of thicknesses. The standard thickness for a back splash depends on the application. The best advice we can give you is rather obvious. The thinner the material the easier it is to form colse to corners and cut with shears or saw. However, the thinner material dents and curls much easier. Also, thinner copper sheet won't hide wall imperfections as well as thicker material.
As a rule of thumb, if the wall covering is flat and/or you need to form the sheet colse to a angle .020 or .032 thickness sheet will work well as a back splash. If the wall is not flat and you don't want to form the material, .040 or .050 will make a very durable bask splash.
One final point to consider is the weight of the sheet. The heavier the sheet the better the mounting adhesive must be or a greater quantity must be used. The easiest way to conclude the weight of copper sheet is to use this method "thickness x width x distance x .322". As an example, copper sheet with the dimensions of .032" x 24" x 36" will weigh (.032 x 24 x 36 x .322) 8.9/lbs.
Good luck with your project.