After graduating from John F. Kennedy High School in Taylor, Michigan, Avery was drafted by the Atlanta Braves in June 1988. He made his first career start on June 13, 1990 against the Cincinnati Reds at Riverfront Stadium and was clobbered, giving up eight runs in 2.1 innings. He ended his rookie year with a record of 3-11 in 21 starts with a 5.64 ERA. Along with Tom Glavine, John Smoltz, and Pete Smith, Avery was christened one of Atlanta's "Young Guns," the name for the pitching staff with great potential but little offensive help.