10:37 baptism which John preached. John’s baptism, accompanied by his preaching of repentance and salvation through the coming Lamb of God (John 1:15-34), marked the beginning of “that word” (compare Acts 10:36-37) which came “preaching peace by Jesus Christ.” Note also Acts 1:22.
10:38 went about doing good. The modern world tends to ridicule “do-gooders,” but if Jesus is our example (I Peter 2:21), we also should go about doing good. “To do good and to communicate forget not: for with such sacrifices God is well pleased” (Hebrews 13:16).