Nyorai kupfuurira kweiyi ndima - Brady akafarikanya basa remuenzaniso rejunior hockey muWHL neMedicine Hat Tigers. Mushure mokunge vawana 81 mumitambo 72 uye vakanyoresa maminitsi anopfuura 100 mu 1985-86, Brady akasarudzwa wechitatu neNew Jersey Devils mu 1986 NHL Entry Draft
. Akadzokera kuJunior, akabva atendeuka pro neAHL's Utica Devils muna 1988/89. Akaita NHL yake yokutanga musi waOctober 5, 1989.