I never "got" Battle Cry of Freedom. I found it tedious, lacking in theme or analysis, and weighed down in irrelevant detail. Instead, I heartily recommend the 8-volume series by Allan Nevins, "The Ordeal of the Union/War of the Union."
I'm not familiar with Battle Cry of Freedom -- I've been focused on the first two levels of the reading list. Your recommendation sounds good (though lengthy). For Civil War reading, I can recommend the Memoirs of Ulysses S. Grant -- that's a wonderful book.