Forgiveness of sins is now related specifically to the sacrificial death of Jesus. Thus the symbolism of the cleansing blood of Christ. It is more than just our sins which were taken upon the cross, there is a sense in which our whole sinful nature was nailed there, such that when we believe in Jesus, we die, our past self-centered life is buried, it dies. This happened at the moment of our repentance, and water baptism symbolically expresses the burial of our past life, ie. going under the water. The moral that Paul brings out of this is that seeing our past life of sin is dead, it is impossible to return to it.
Water baptism can symbolically express both a cleansing and a burial.
When related to Evangelism. In the New Testament, the person who responds to the gospel in repentance is baptized on the spot. The person performing the baptism. We are told that on the basis of the faith of the Philippian jailer, his household was saved ie. Certainly the unbelieving partner has a better chance of conversion through their proximity to God via their partner's faith.