NAACP
NAACP v Alabama was important because it would have prohibited the NAACP from operating in the state of Alabama. The NAACP won the case and it was a big victory for civil rights.
Thurgood Marshall, who later became the first African-American US Supreme Court justice.
University of California v. Bakke
Thurgood Marshall was lead counsel for the NAACP-sponsored case Brown v. Board of Education, (1954), and its follow-up case Brown v. Board of Education II, (1955). He argued 32 civil rights cases before the US Supreme Court, and won 29 of them. In 1967, President Lyndon Johnson appointed Marshall to the US Supreme Court, making him the first African-American justice in the Court's history.
The civil rights movement began in the mid 1950s with the court case Brown vs. Topeka board of Education. This was in 1954 and the NAACP mainly did the work in this case and also in the Montgomery Bus Boycott. Overall The NAACP started the movement.
The NAACP organized lawsuits to end "separate but equal." The landmark case of Brown v. Board of Education of Topeka in 1954 was funded and organized by the NAACP after the Topeka chapter of the NAACP decided that that particular case would be most likely to reach a favorable conclusion in the US Supreme Court.
Trial Court
You may be asking who argued Brown v. Board of Education,(1954) before the US Supreme Court. The lead counsel for the Petitioner (Brown, et al.) was Thurgood Marshall, who later became the first African-American to serve on the Court.Attorney Charles Hamilton Houston, former Dean of Howard University Law School, hired Marshall to work with the NAACP. Thurgood Marshall later became a founder of the NAACP Legal Defense and Education Fund, an independent, but related, arm of the national organization responsible for much of the legal battle for African-Americans' civil rights.The NAACP and the NAACP Legal Defense and Education Fund brought many cases to the US Supreme Court under the leadership of prominent African-American attorneys. Thurgood Marshall was, perhaps, the best remembered by history, but was by no means the only lawyer working for civil rights, nor was Brown the only case the NAACP sponsored.For more information, see Related Questions, below.
The authority to hear a case is called jurisdiction. The court with authority to try the case, or hear it first, has original jurisdiction; the court(s) that review the case on appeal have appellate jurisdiction.If the case is remanded for a new trial (or reheard, I suppose), it returns to the court of original jurisdiction.
If the US Supreme Court is the first to hear a case, the Court has original jurisdiction.
The trial court.Added: The court of original jurisdiction.