To whom is baptism to be administered?

Answer

Baptism is to be administered to all those who actually profess repentance towards God (; ; ; ; ; ), and faith in our Lord Jesus Christ, and to none other.

Read the 6 proof texts (KJV)

Acts 2:38: Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Matthew 3:6: And were baptized of him in Jordan, confessing their sins.
Mark 16:16: He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
Acts 8:12: But when they believed Philip preaching the things concerning the kingdom of God, and the name of Jesus Christ, they were baptized, both men and women.
Acts 8:36-37: ³⁶And as they went on [their] way, they came unto a certain water: and the eunuch said, See, [here is] water; what doth hinder me to be baptized? ³⁷And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
Acts 10:47-48: ⁴⁷Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? ⁴⁸And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.