I would say that none of their roles are mutually exclusive. But, certain functions of God are more closely associated with different persons of the trinity.
The Spirit serves as teacher. (Psalm 32:8, John 14:26) The Greek word translated "teacher" in the ESV is Parakletos, which can mean "legal counsel". The Spirit dwells in all believers. (Exodus 29:45, 1 Corinthians 3:16) He guides into all the Truth. (Psalm 25:9, John 16:13-15)
The Son has taken on humanity as serves as our high priest and mediator. (Leviticus 8:9, Hebrews 7:3) The Son is also a translation of God's nature as the Word (Ezekiel 1:3 Micah 1:1 John 1:1) He created and sustains the universe. (John 1:2, 3, Colossians 1:16, Hebrews 1:3 10-12)
The Father is responsible for our election. (Deuteronomy 7:6, Ephesians 1:3, 4) He draws us to the Son. (Exodus 19:4, John 6:44) And the Father is the one who glorifies us and all of creation. (Isaiah 6:3, Habakkuk 2:14, John 17:24) And all of the glory goes back to Him. (John 5:23, 1 Corinthians 8:6, Philippians 4:20)