Peca began his junior career with the Sudbury Wolves of the Ontario Hockey League (OHL) after they selected him in the first round of the 1990 player draft. He was traded to the Ottawa 67's where he blossomed into one of the league's top offensive players. He was drafted in the second round, 40th overall, by the Vancouver Canucks in the 1992 NHL Entry Draft. He made his NHL debut with the Canucks in the 1993–94 season, playing four games before cracking the lineup as a regular in the lockout-shortened 1994–95 season. He would then be traded to the Buffalo Sabres during the 1995 NHL Entry Draft as part of a package that sent Alexander Mogilny from Buffalo to Vancouver.