It most depends on personal preference but there are a few pros and cons associated with printing glassy or matter postcards.

Glossy

Glossy postcards have a smooth and shiny finish and look very polished.  This coating allows for a crisper looking image, especially when the card is filled with vivid imagery.  Glossy cards are great for postcards that have lots of colorful images.  Glossy postcards will also be processed through the United States Postal Services’ machines with less damage.

Matte

Matte cards have a subtle shine and offer a more professional look.  Matte postcards are more commonly used in cards that are predominately text based or where text is the focus of the card.  The matte finish allows high contrast between text and images and increases the readability of the card.  This finish also enhances white space within the card.

Ultimately the choice is yours and you cannot really go wrong with either, yet the subtle differences between a matte and gloss could give your postcard the perfect look and feel that will grab the recipients attention.