Sinolingua puts out a four-volume series called “Series of Short Chinese
”. Each volume has roughly 15 stories or articles, complete with vocabulary list and grammar explanation. Readings
Peking University Press puts out a book called “Reading Chinese Through Humorous Stories”, consisting of 60 stories arranged from very short to quite long, each with vocabulary list.
The DeFrancis series, Beginning, Intermediate & Advanced Chinese Reader are "graded".