The baptism of fire that John is referring to is a fulfillment of a prophecy from Joel. It was fulfilled at Pentecost (Acts 2) and later with Cornelius and his family (Acts 10).
Paul's mention of "one baptism" in Ephesians 4 is clearly the baptism that puts us into the "one body", which is the baptism administered to the people in Acts 2:38-41.
When a person believes, has repented of their sins, confessed that Christ is the Son of God, and been baptized for the remission of sins, they receive the Holy Spirit(Acts 2:38).
***When a person believes, has repented of their sins, confessed that Christ is the Son of God, and been baptized for the remission of sins, they receive the Holy Spirit(Acts 2:38).***
Cornelius received the Holy Spirit before baptism. When Peter saw that he and those with him had received the Spirit he said...
"Can anyone withhold water for baptizing these people, who have received the Holy Spirit just as we have?"
He saw clearly that they had been born again - proof being the reception of the Spirit.
John 3:6
That which is born of the flesh is flesh; and that which is born of the Spirit is spirit.
Is baptism important? YES! Is it a requirement for being born again - No. The story of Cornelius proves that.