John Chrysostom
"Repent," he says, "and let every one of you be baptized in the name of Jesus Christ."
He does not yet say, "Believe," but, "Let every one of you be baptized," because they were receiving faith in baptism.
Then he shows the benefit of baptism: "for the remission of sins; and you shall receive the gift of the Holy Spirit."
If you will receive the gift, and if remission of sins is given through baptism, why do you delay?
[...] The former words were spoken in order to bring them to faith. These words showed what the believer must do.
He did not speak about the Cross, but said, "Let every one of you be baptized in the name of Jesus Christ."
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He does not continually remind them of the Cross, lest he seem to reproach them. He simply says, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins."
In earthly courts the law acts otherwise. But in the work of preaching, the sinner is saved when he confesses his sins.
See how Peter did not omit what was more important. Having first spoken of grace, he then added this also: "and you shall receive the gift of the Holy Spirit."
His word was trustworthy because they themselves had received the Spirit.
He first speaks of what is easy and gives a great gift. Only then does he lead them toward life, knowing that what they had already tasted of so many blessings would stir their zeal.
Since the hearer wished to know the substance of his many words, he adds this too, showing that this is the gift of the Holy Spirit.
Thus those who received his word approved what he had said, though his words were full of fear. After approving them, they came to baptism.