My late mother-in-laws maiden name was Schechter and as you said it is a common name so it is very difficult to find. This Schechter family came as far as I know from Austria and emigrated in the late 1890's and lived in what became known as the Crown Height section of Brooklyn. The patriarch of the family was Selig Schechter and his wife's name was Annie.
All this being said do you happen to even know where in Brooklyn your Schechter family lived. Other than finding information on my husband's Schechter great grandparents had two children-Max who married Bertha Spindel and Cecile who married Max Rosenbloom I don't really know much else. Does this help and can you provide me with whatever you might know.