Best, who was trained on piano, trumpet, and bass, concentrated on the drums starting in 1943. Between 1943 and 1944 he worked with Ben Webster, and subsequently with Coleman Hawkins (1944–1945), Illinois Jacquet (1946) and Chubby Jackson. The drummer was known to sit in at Minton’s Playhouse. He took part in a recording with George Shearing in 1948 and was a founding member of his Quartet, remaining there until 1952. In 1949 he played on a recording with Lennie Tristano and also recorded later with Lee Konitz. After a car accident he played in 1954 with Artie Shaw, and then in a trio with Erroll Garner (1955–1957). Following this he played with Phineas Newborn, Nina Simone, Billie Holiday and Tyree Glenn. In 1962 he appeared on the first release by Sheila Jordan. He suffered from paralysis after this and was no longer able to play; he died after falling down a staircase in a New York City Subway station.