Hamilton was drafted by the Milwaukee Brewers in the 11th round of the 1986 Major League Baseball draft and signed a contract with them on June 12, 1986. He made his professional debut that season with the Helena Gold Sox of the Rookie-level Pioneer League, hitting .391 in 65 games. In 1987 with the Stockton Ports of the Class A California League, he hit .328 in 125 games with eight homers and 61 RBI, on a team that was rated one of the top farm teams in Brewers history. He began 1988 with the Denver Zephyrs of the Class AAA American Association, where he hit .325 in 72 games.