The civil rights movement was defined in its beginnings by its nonviolent approach to change. This became a defining characteristic of the movement mainly due to the involvement of Dr. Martin Luther King. Dr. King admired the approach that Mohandas Ghandi had taken to achieve the independence of India, and he wanted to replicate this approach in the United States. Many of the initial victories of the movement were due to this approach.
However, as time passed and the movement grew stronger, their strategy became more radical in some cases. This was most likely due to the fact that many people believed change to be happening in a very slow way. They wanted to achieve more meaninful change faster. This led to the escalation and radicalization of the movement.
I believe the best strategy was the nonviolent approach. The lack of violence ensured that the protesters were always seen as being on the side of the law. Therefore, it only highlighted how unfair and unjust the law was. Moreover, this approach was more likely to be appreciated by a wide range of people.