In the context of the writer organizing their essay to show how choices made during and after Reconstruction continue to impact people today, the most appropriate choice is cause and effect. This text structure allows the writer to explore how specific decisions and policies from that era led to certain consequences that can still be observed in contemporary society.
While compare and contrast, problem and solution, and other structures could also be applicable in different contexts, cause and effect is specifically geared towards discussing the relationship between historical actions and their long-term impacts.