McNeely first attended Decatur Baptist Junior College, where he set high-scoring records on the school's basketball team. He transferred to Texas Wesleyan University in 1940, but his "shot-crazy" style created doubt as to how well he could fit on the team. During his first season at Texas Wesleyan in 1940–41, McNeely established himself as one of the most talented players on the team and was named team captain for the 1941–42 season. He helped guide Texas Wesleyan to an undefeated record during the 1941–42 regular season, with the team's only two defeats coming in the postseason against Sam Houston State in the Southwestern AAU Tournament and San Diego in the Kansas City National Intercollegiate Basketball Tournament.