It might be good to read about Dr. King's Chicago Campaign before reading Hansberry's work. Dr. King's movement in the North was designed to tackle an adversary that was different than the Klansmen of the South, but still reflected the same inhumanity:
King believed that turning SCLC’s attention to the North made sense: ‘‘In the South, we always had segregationists to help make issues clear.… This ghetto Negro has been invisible so long and has become visible through violence’’ (Cotton, 26–28 August 1965). Indeed, after riots in Watts, Los Angeles, in August 1965, it seemed crucial to demonstrate how nonviolent methods could address the complex economic exploitation of African Americans in the North.
I think that this context makes perfect sense to read about before starting to analyze Hansberry's work. Bringing out the social context in which Hansberry writes her work along with the political struggles of the time period allows to see how the drama reflects the realistic condition of the time. At the same time, it helps to evoke the notion of discrimination that is such a part of the time period and impacts all of the characters. Reading about Dr. King's work in the Chicago Movement helps to bring out a social and political dimension to what is being illuminated through the drama.