Just a little key: Purple is my words, Red is Jesus' words, Black is the Bible's words, and Blue is the words of the non-denominational Bible Study I reference to ("Into His Marvelous Light" (C) Galen Walters)
John 3:5 - Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God. (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 recieve the gift of the Holy Ghost. (KJV)
Therefore, if Jesus said unless a man be born of the water and the Spirit (that is, baptized both in water and filled with the Holy Spirit) he/she will not enter into Heaven, and Jesus told the Disciples what to tell people, and Peter told the people that in order to be filled with the Holy Spirit one must repent and be baptized. Therefore, believing must be put together with acts.
There is a passage in a Bible Study I did that addresses your direct question. This is a non-denominational Bible study that is called "Into His Marvelous Light".
John 3:1-8 1Now there was a man of the Pharisees named Nicodemus, a member of the Jewish ruling council. 2He came to Jesus at night and said, Rabbi, we know you are a teacher who has come from God. For no one could perform the miraculous signs you are doing if God were not with him. 3In reply Jesus declared, I tell you the truth, no one can see the kingdom of God unless he is born again. 4How can a man be born when he is old? Nicodemus asked. Surely he cannot enter a second time into his mother's womb to be born! 5Jesus answered, I tell you the truth, no one can enter the kingdom of God unless he is born of water and the Spirit. 6Flesh gives birth to flesh, but the Spirit gives birth to spirit. 7You should not be surprised at my saying, You must be born again. 8The wind blows wherever it pleases. You hear its sound, but you cannot tell where it comes from or where it is going. So it is with everyone born of the Spirit. (NIV)
The Lord told Nicodemus that everyone who wanted to see or enter the kingdom of God must be born again of water and the Spirit.
John 3:16-21 16For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. 17For God did not send his Son into the world to condemn the world, but to save the world through him. 18Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God's one and only Son. 19This is the verdict: Light has come into the world, but men loved darkness instead of light because their deeds were evil. 20Everyone who does evil hates the light, and will not come into the light for fear that his deeds will be exposed. 21But whoever lives by the truth comes into the light, so that it may be seen plainly that what he has done has been done through God. (NIV)
Jesus also told Nicodemus that whosoever believeth in Him shall have eternal life. Jesus mentioned two seemingly different requirements for salvation, one being born again, the other believing. Yet, this is not a contradiction. The next scripture explains how believing is related to experiencing the birth of the Spirit...
John 7:38-39 38Whoever believes in me, as the Scripture has said, streams of living water will flow from within him. 39By this he meant the Spirit, whom those who believed in him were later to receive. Up to that time the Spirit had not been given, since Jesus had not yet been glorified. (NIV)
Here, we discover that if we believe on Him we will receive His Spirit. We find that scriptural belief is more than just a change in the way we think. It also results in a scriptural experience. Faith motivates us to obey, and obedience brings God's acceptance and blessing.
You mentioned Mark 16:16. I'm going to post Mark 16:16-17, and these words are spoken by Jesus.
16 He that believeth and is baptized shall be saved; but he that believeth not shall be damned. 17 And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues. (KJV)
Jesus is saying here that those who believe will follow his word, and those who follow his word (thus being baptized, repenting, and being filled with the Holy Ghost) will speak in new tongues. Speaking in new tongues is initial evidence of being filled with the Holy Spirit. Acts 2:4 - And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance.
Many people today, however, argue that the plan of salvation as mentioned in Acts 2:38 is only in that time, and that people today do not need to follow that, nor will people speak in tongues when filled with God's Spirit. However, in Acts 19, Paul spoke to those people who were baptized by John the Baptist, and Paul told them they needed to be re-baptized in God's new plan of salvation.
Acts 19:3-5 - And he [Paul] said unto them, Unto what then were ye baptized? And they said, Unto John's baptism. Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus. When they heard this, they were baptized in the name of the Lord Jesus. (KJV)
See, God didn't want only those mentioned on the day of Pentecost to be baptized and filled with the Holy Spirit... he wanted people for ever and always to follow this plan.
Acts 2:39- 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. (KJV)
Therefore, yes, in order to be saved one must believe. But if you believe in God and His word, then you believe in all that God commanded his people to do, including repenting, being baptized, and being filled with the Holy Spirit.
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