Moore, born and raised in the western Sydney suburb of Doonside, where he attended Crawford Public School and Doonside High while playing for the Doonside Hawks Soccer Club, is best known for his two spells with Scottish Premier Division / Scottish Premier League club Rangers. Having graduated through their youth system, he made 252 appearances for the Glasgow based club from 1993 to 2005, punctuated with a season in England with Crystal Palace in the 1998–99 First Division. In his time at Rangers he became team captain and won numerous domestic league and cup honours, including making 44 appearances and scoring four goals in their 2002–03 Treble-winning season.