The Museum of Mississippi History is the companion to the Civil Rights Museum next door, and the two were designed to be visited together. It covers 15,000 years of human presence in what is now Mississippi: the Choctaw and Chickasaw, the French and Spanish on the Gulf coast, the cotton economy and slavery, the Civil War, Reconstruction, the great twentieth-century migrations.
The exhibits are well-curated and unsentimental. A single ticket gets you into both museums and most visitors do them in one long visit — plan for at least three hours combined, and don't try to do it on a tight schedule.