Brady enjoyed an exemplary junior hockey career in the WHL with the Medicine Hat Tigers.
After scoring 81 points in 72 games and registering over 100 penalty minutes in 1985–86, Brady was chosen third overall by the New Jersey Devils in the 1986 NHL Entry Draft.
[1] After just 29 games in 3 seasons in which Brady struggled with his confidence, the Devils organization gave up on him, and he was traded to the expansion Ottawa Senators for future considerations on September 3, 1992.
Brady fell out of favour with the Senators organization, and was signed as a free agent by the Dallas Stars in December, 1993, though he was chiefly a farmhand for his new team.
In total, Brady played in 89 NHL games, scoring 9 goals and 22 assists for 31 points and 95 penalty minutes.