Paper selection is a very important part of the design process for a printed communication piece. Unfortunately, in many cases this element is left behind in the process, and the final decision depends more on the available budget.
There are many elements to consider when selecting paper stock: Coated or Uncoated, Textured or Smooth, Bright or Dim, Glossy or Dull, Thick or Thin, Opaque or Transparent, White or Color, etc.
One of the basic decisions is Coated vs. Uncoated:
Uncoated papers are more textured and porous, affecting the way ink lays on the paper surface. Inks tend to spread out more, which would not work well for a design with very small, thin, or sharp details. Images would be softened, and colors would not be very saturated.
Coated papers are smoother. Their surface allows a sharper and more detailed result, and brighter and more saturated colors can be obtained.
If you are a designer or a client working with a designer, research paper types, talk with your printer to learn about possibilities, and make the best choice depending on who will use this piece, how it will be used, and what is the intended message.
Glossy papers can make reading harder in certain lighting conditions, for example, but can be good in some cases because of the more shiny end results and the more saturated colors obtained.
There is no unique formula for a successful choice. Talk with your designer or client, and may the best paper win!