the first mention of baptism in holy scripture, it is in water.
Also, consider the following.
Act 10:45, And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost.
Act 10:46, For they heard them speak with tongues, and magnify God. Then answered Peter,
Act 10:47, Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we?
Act 10:48, And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
They already had the Holy Ghost but Peter commanded them to be baptized. Was this in the Holy Spirit? Because they were already given the Holy Spirit.
I think that you can see that this baptism was in water.
It sets before us a precedent as to what baptism is. Baptism is in water.
Consider also the following.
1Pe 3:20, Which sometime were disobedient, when once the longsuffering of God waited in the days of Noah, while the ark was a preparing, wherein few, that is, eight souls were saved by water.
1Pe 3:21, The like figure whereunto even baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ:
Here it is clearly speaking of being saved in water baptism.
Hebrews 9:10 KJV - [Which stood] only in meats and drinks, and divers washings, and carnal ordinances, imposed [on them] until the time of reformation.
Diverse washings are baptisms and can be found in: Exodus 29:4 KJV - And Aaron and his sons thou shalt bring unto the door of the tabernacle of the congregation, and shalt wash them with water.
Aaron was a priest and had to be cleansed for the priesthood.
Israel was to be a kingdom of priests:
Exodus 19:6 KJV - And ye shall be unto me a kingdom of priests, and an holy nation. These [are] the words which thou shalt speak unto the children of Israel.
Israel had to be baptized to be a cleansed priesthood prepared for the kingdom:
Mark 1:4 KJV - John did baptize in the wilderness, and preach the baptism of repentance for the remission of sins.
The gospel of the kingdom in which they would be priests was preached by Jesus and the twelve:
Matthew 9:35 KJV -And Jesus went about all the cities and villages, teaching in their synagogues, and preaching the gospel of the kingdom, and healing every sickness and every disease among the people.
Mark 1:15 KJV - And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel.
In Acts 10:45-48 that you cited the Gentiles believed the gospel of the kingdom and were baptized to be cleansed to enter the kingdom (not as priests however).
In regard to 1 Peter 3:21-21.....Peter was talking to Israel.
Israel was saved by baptism to enter the kingdom, if they did not get baptized they would not enter:
Mark 16:16 KJV - He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
The resurrection of Christ in 1 Peter 3:21 assured Israel he would sit on the throne of David in the kingdom and they would be saved by baptism to enter the kingdom:
Acts 2:30 KJV - Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne;
