Costa played several sports at St. Joseph's Preparatory School in Philadelphia. When he graduated from high school, he held virtually every passing record in the city's history including completions in a game (27), season (196), and career (373); as well as yards passing in a season (2547) and career (4760); and touchdowns in a season (24) and career (35).[1]The Philadelphia Inquirer named Costa as the quarterback on their all-decade high school team for the 1980s.[2] After being recruited nationally, he chose to play football at the University of Miami in Coral Gables, Florida.
In his first two seasons with the Hurricanes, Costa was a backup quarterback, behind starter Gino Torretta. In his final two seasons, Costa was the starter for most of Miami's games, including a memorable win against rivalFlorida State on October 8, 1994.[3] The 1994 Hurricanes reached the Bowl Coalition's championship game for that season, the 1995 Orange Bowl, where Costa passed for 248 yards (18-for-35) with two touchdowns and one interception, as Miami lost to Nebraska, 24–17.[4] Costa finished his college career with a record of 19–3 as a starter; he appeared in a total of 34 games for the Hurricanes, passing for 4256 yards and 22 touchdowns.[5]