Just because Acts is transitional does NOT mean that it is not doctrinal for Christians today. This is the error made by the Hyper-Dispensationalists with their heresies. So let's look at Acts 2: 38 IN CONTEXT and see that everything there is fully applicable to the Gospel, and to churches today.
ACTS 2: HOW A CHURCH IS FORMED AND FUNCTIONS
THE GOSPEL IS PREACHED
36 Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ.,,, 40 And with many other words did he testify and exhort, saying, Save yourselves from this untoward generation. [Note: the death, burial, and resurrection of Christ was preached, and then He was declared to be BOTH Lord and Christ. Therefore Christ must be received as Lord in order to be saved]
SINNERS ARE CONVICTED BY THE HOLY SPIRIT
37 Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do? [Note: Whenever the true and full Gospel is preached, the Holy Spirit is there to convict and convince sinners]
FAITH AND REPENTANCE ARE JOINED TOGETHER
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. [Note: Repentance is for the remission of sins,. While faith is not mentioned here, it is implied with "in the name of Jesus Christ" who is always the object of faith. Baptism is not for regeneration, but to confirm that souls have been regenerated]
THE HOLY SPIRIT IS PROMISED TO BELIEVERS UNDER THE NEW COVENANT
39 For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call. [Note: while this promise was to Israel, Gentiles are included under the Abrahamic Covenant. All those who believe receive the gift of the Holy Ghost (Spirit), also called baptism with the Holy Spirit]
FAITH IN CHRIST IS GENERATED BY THE GOSPEL, AND SOULS ARE SAVED. BAPTISM FOLLOWS
41 Then they that gladly received his Word were baptized: and the same day there were added unto them about three thousand souls. [Note: to "gladly receive his Word" is to have faith in Christ, since He Himself is the Gospel. Salvation is by grace through faith in Christ and His finished work of redemption. And water baptism must follow immediately or shortly thereafter]
THE REDEEMED ASSEMBLE TOGETHER FOR THESE THINGS
42 And they continued stedfastly in the apostles' doctrine and fellowship, and in breaking of bread, and in prayers. [Note: Jesus said "teaching them to observe all things whatsoever I have commanded you", and this is seen here]
THE IMPACT OF THE CHURCH IS FELT BY OTHERS
43 And fear came upon every soul: and many wonders and signs were done by the apostles. [Note: the preaching of the Gospel also results in fear of disobedience to the Gospel. Therefore Hell cannot be excluded from the Gospel]
THE CHURCH FUNCTIONS AS A FAMILY IN CHRIST
44 And all that believed were together, and had all things common; 45 And sold their possessions and goods, and parted them to all men, as every man had need. [Note: this fulfils the Second Greatest Commandment]
LIVES ARE TRANSFORMED THROUGH THE HOLY SPIRIT
46 And they, continuing daily with one accord in the temple, and breaking bread from house to house, did eat their meat [food] with gladness and singleness of heart, [Note: the redeemed are "new creatures in Christ" and their lives reflect this]
THE CHURCH HAS A POSITIVE SPIRITUAL IMPACT ON THE WORLD
47 Praising God, and having favour with all the people. And the Lord added to the church daily such as should be saved. [Note: God desires the salvation of souls daily]