A Nation Under Our Feet is on my short list to read, but right now I'm trying to find an audible book so I can listen on my way to/from work.
Feel free to suggest all good books that cover that era, I'll check if they're on Audible myself.
I recently read The Wars of Reconstruction and Slavery by Another Name and finished the lecture portion of David Blight's Yale course on The Civil War and Reconstruction and I'd like to fill in gaps I'm missing before The Civil Rights Movement. Specifically history of the lives of black Americans during that period.
Here are my recommendations, these are all fairly general and not too academic. If you want more recommendations, as well anything more specific (state/region or era) I can dig more out for you.
Reconstruction: America's Unfinished Revolution 1863-1877 by Eric Foner. Definitive book on Reconstruction.
The Warmth of Other Suns: The Epic Story of America's Great Migration by Isabel Wilkerson. Definitive book on the Great Migrations.
Freedom Struggles: African Americans and World War I by Adrienne Lentz. Definitive book on African-Americans and World War I.
The Strange Career of Jim Crow by C. Vann Woodward. A bit more historiographical. Called "The Historical Bible of the Civil Rights Movement" by Dr. Martin Luther King Jr. This book lays down the history and development of Jim Crow laws. Short and easy to read, very important.
The Crucible of Race: Black White Relations in the American South Since Emancipation by Joel Williamson. Thick, well written, detailed history of the 1865-1915 era. Very good for understanding African-American social life and cultural development.
Not Alms but Opportunity: The Urban League and the Politics of Racial Uplift 1910-1950 by Toure Reed. Good look at Civil Rights Organization building and use during the stated period.
Parting the Waters: America in the King Years 1954-1963 by Taylor Branch. First of three books by Dr. Branch. All very, very important for understanding the grand national Civil Rights Movement. After the period you're asking for, but this is a good beginner book for the mainstream 1954-1968 Civil Rights Movement.
Hammer and Hoe Alabama Communists During the Great Depression by Robin D.G. Kelley. Another look at the political and social lives of African Americans during the Great Depression. A fantastic work and relatively short for an academic piece.
Booker T. Washington's autobiography Up From Slavery gets my vote. It is in the public domain and fairly short. Also, Washington's role often gets truncated to a few-sentence narrative, e.g. - "his faction promoted accommodation." That's not wrong, but it's also not the whole story. He and Dubois really should be read at the same time, imho.