It's not always the same. Cornelius' conversion was in a different order. He was born again and lived a holy (repentant) life before Peter preached to him. They were filled with the Spirit and then baptized.
Of course; I was merely going by the text that was at hand.
btw, when Cornelius and friends were converted, it was a special circumstance because God had to go to some drastic measures in order for the circumcision group to accept Gentiles into the body of Christ...God proved that Gentiles could be Christians by giving them the Holy Ghost before they were baptized...which was not the normal order of things, but a necessary work so that the circumcision would not be able to deny the inclusion of Gentiles into the church.
Normally, things go in the order that I told you:
1) preaching 2) repentance 3) belief 4) baptism in Jesus' name 5) remission of sins 6) the gift of the Holy Ghost 7) living a holy life.
But in Cornelius' instance it was 1) repentance 2) living a holy life 3) preaching 4) belief 5) the gift of the Holy Ghost 6) baptism in Jesus' name 7) remission of sins.
This just blows my mind because some things that go after are things that I would think to be causal to some of the things that go before.
It just goes to show that we can't put God in a box!
But, again, I would say, that the case with Cornelius and friends was a special circumstance that had to do with God's taking special measures to ensure that Gentiles would be included in light of the opposition of those in the circumcision group.