Fish is considered pareve, it's neither meat nor dairy so it can be served with either kind of food. Meat requires a complex system of slaughtering rituals to make it kosher while all fish are kosher as long as it has fins and scales so it's both economical and convenient to consume more fish (particularly preserved fish).

Most importantly though, salt fish is mentioned in a discussion dealing with the kashruth of dishes cooked by non-Jews. The rabbis decreed that salt fish was kosher even if it had been made by gentiles since they are not actually cooked and thus not considered bishul akum. In the Old World the fish of choice was actually herring. They are very plentiful in the Baltic Sea and can be easily preserved in barrels (by anyone) for shipping to inland areas (it's not just the Jews, practically every country in Central and Eastern Europe consume large quantity of herrings). Salted herrings were probably the only ready-to-eat food Jews were allowed to buy from non-Jews. White fish like carps were also common since they are available in river streams and can be easily caught and eaten without necessary kashruth rituals.

Salmon was not traditionally eaten by Jews living in Central and Eastern Europe. It only became associated with Jewish cuisine after significant amount of Jewish diaspora immigrated to the Great Britain and United States where salmon was much more plentiful.

Source: In Search of Plenty: A History of Jewish Food by Oded Schwartz