Mezue ahịrịokwu na-esonụ: Brady nwere ọmarịcha ọrụ hockey na WHL na Medicine Hat Tigers. Mgbe o nwetara akara 81 na egwuregwu 72 ma debanye aha ihe karịrị nkeji 100 na 1985-86, Brady bụ onye nke atọ nke New Jersey Devils họọrọ na
1986 NHL Entry Draft. A laghachiri ya na nwata, wee gbanwee pro na AHL's Utica Devils na 1988/89. O mere NHL mbụ ya n'abalị ise nke ọnwa Ọktoba n'afọ 1989.