Complex sentence: Her true professional career began at that 1959 Newport Folk Festival; following that appearance, she recorded her first album for Vanguard, "Joan Baez" (1960), produced by Fred Hellerman of The Weavers, who produced many albums by folk artists.
Split into simpler sentences: Her true professional career began at that 1959 Newport Folk Festival. Following that appearance, she recorded her first album for Vanguard, "Joan Baez" (1960), produced by Fred Hellerman of The Weavers, who produced many albums by folk artists.