She was born as Florence Beatrice Smith to Florence (Gulliver) and James H. Smith on April the ninth, 1887, in Little Rock, Arkansas, one of three children in a mixed-race family. Despite racial issues of the era, her family was well respected and did well within their community. Her father was a dentist and her mother was a music teacher who guided Florence's early musical training. She had her first piano performance at the age of four and had her first composition published at the age of 11.
By the time she was 14, Florence had graduated as valedictorian (scholar) of her class. After high school, she later enrolled in the New England Conservatory of Music in Boston, Massachusetts with a major in piano and organ. Initially, she identified as Mexican to avoid the prejudice people had toward African Americans at the time. At the Conservatory, she studied composition and counterpoint with composers George Chadwick and Frederick Converse. Also while there, Smith wrote her first string trio and symphony. She graduated in 1906 with honors, and with both an artist diploma in organ and a teaching certificate.
Smith returned to Arkansas, where she taught briefly before moving to Atlanta, Georgia, in 1910. There she became the head of the music department of what is now Clark Atlanta University, a historically black college. In 1912, she married Thomas J. Price, a lawyer. She moved back to Little Rock, Arkansas, where he had his practice. After a series of racial incidents in Little Rock, particularly a lynching of a black man in 1927, the Price family decided to leave. Like many black families living in the Deep South, they moved north in the Great Migration to escape Jim Crow conditions, and settled in Chicago, a major industrial city.