Question invites thematic approach as means of assessing 'effectiveness' e.g. political, economic and social To what extent question encourages evaluation and comparison
Arguably Martin Luther King was the most effectively civil rights leader for the advancement of African American civil rights due to the scale and magnitude of change that MLK encouraged. MLK's peaceful methods helped unite a, for the most part, previously fragmented movement and in doing so manged to secure crucial rights for African Americans as well as drawing an unprecedented amount of attention to the civil rights movement. The pressure exerted upon the government by MLK was sufficient to necessitate real change as is marked by numerous legislation successfully passed by LBJ such as the 1964 Civil Rights Act and the 1965 Voting rights bill securing de facto rights for African Americans that they had been denied despite their supposed granting de jure through the 14th and 15 constitutional amendments.
To provide a balanced answer the impact of other civil rights leaders can be noted including Du Bois as well as Marcus Garvey and Malcom X. A case could be made that Malcom X was more effective at securing economic and social rights for African Americans where as MLK predominantly focused on political rights which arguably were less immediately important to many African Americans living in poverty, particularly in the North.