I believe
Romans 6:3 is water baptism for a several reasons.
One, it's some kind of baptism, which gives it a 50/50 chance of being water baptism.
Two, it is a baptism into death, not life, and the Spirit is life.
Three,
Romans 8 is all about Spirit baptism, leading me to think
Romans 6 is about water baptism.
Four, it fits the OT typology and message of the Gospel, including
Acts 2:38.
More than anything, however, I think
Romans 6 is not just talking about a here and now temporal solution to sin, but is also indicating what happens to the saved at check-out time. They shall walk in newness of life in New Jerusalem. So when it talks of resurrection, I don't automatically only think gift of the Holy Spirit, I also think Glorification, much in the same way Christ was glorified and ascended (something that hasn't happened to us, yet).
Regarding Cornelius, the Apostles and Elders in Jerusalem, when hearing the news, said that God had granted them repentance unto life. I take this to mean that God had granted them a sufficient level of repentance in order to be saved, and sealed that repentance with proof, i.e. the Holy Spirit, if for no other reason than to convince the circumcised believers who went with Peter.
I don't take it to mean that should they have rejected Peter's command to be baptized in the name of the Lord Jesus, that all would have been A-OK between them and God.
The body of sins still needed to be destroyed, else there is no rational justification for the command/order. We must assume that either Peter was being led of his flesh and didn't know what else he should have done/said (i.e. he was flying by the seat of his pants), or Peter was giving a command/order from the Holy Spirit by the Lord Jesus.
If the first is true, then what's the point of trusting much that's in the Bible, especially as it relates to Simon Peter?
If the second is so, then we must realize that Christ had a definite, salvific intention in having His Apostle command/order them to be baptized in His name.
We might not understand it all (I don't pretend to do so) but I think we can at least declare this much.
I hope I helped!