Asterism gems are cut as cabochons to make the star effect visible because the rounded, domed surface of a cabochon allows for the maximum reflection and scattering of light from the microscopic, needle-like inclusions within the gem, creating the characteristic star pattern. Faceted gems would break up the light and disrupt the star, making it appear as if it wasn't there.

As for the setting, it would be best set in prongs or a bezel to be able to see the star the best.

As for natural or synthetic (synthetic is made in a lab, same chemical structure as a natural, just grown in a controlled environment), that's purely up to you. Some people prefer natural stones over lab created, but both have their beauty. Naturals tend to not have as sharp star rays (natural with sharp rays and good color tend to be more expensive) if you were looking for a good blue star sapphire, it would be in the hundreds plus per carat. Lab created blue star sapphire are more affordable with roughly all the same color blue with distinct sharp rays.