ハワイ・ウィンターリーグ
Barrett was born in Atlanta. He attended Pace Academy, where he excelled in baseball. During his senior year, Barrett won Atlanta's Gatorade's Player of the Year, and was named to the All-USA High School and First Team High School All-Americans All-star teams. He was considered to be one of the top draft prospects that year, and declared eligibility for the upcoming Major League Baseball Draft shortly after graduating from high school. Barrett initially signed a letter of intent to play college baseball at Clemson. The Montreal Expos selected Barrett as the 28th overall selection in the draft. He spent the next three years in the minors, playing in the Gulf Coast, South Atlantic, Hawaii Winter Baseball, and Florida State Leagues, during which he was converted from a shortstop to a catcher. His Minor League Baseball career was highlighted in , when he scored 57 runs and recorded 113 hits as a member of the Delmarva Shorebirds.