There is arguably a "trinitarian shape" to the New Testament at least in terms of one potential outcome, but how solid is it. This argument likely works as much against Unitarian Christians as for them - look at http://www.unitarianchristian.net to see how narrow this can get. It takes some explaining, via the parallel argument around the apparent divinity of Christ (thus utting to one side the Holy Spirit aspect).
The debate about Christ and divinity runs parallel with the Trinity. As Christianity developed the Alexandrians and Antiochians had a disagreement. The Antioch side were interested in the two natures of Christ, particularly to include his humanity, whilst the Alexandrians focussed more in the Trinity and as a result emphasised divinity. From them came the Monophysites, who did this. Whether the danger is too much focus on divinity or the two natures, the issue of the Trinity is having God the son as a doctrinal position, as much as son of God (which can be subordinate). Always the debate about humanity and divinity affect this trinitarian discussion. The locus of the debate begins in the New Testament and then subsequent development.
Paul does not agree with the Nicene creed. 1 Corinthians 15: 27-28 has it that the Son will yield up the Kingdom of God, whereas the creed states that Christ's Kingdom shall have no end. Thus Christ is subordinate to God. Yet Paul does have strong titles for Jesus - Christ, Lord and the Son. These are well stronger than the human and messianic understandings of the Church in Jerusalem led by Peter. The Pauline titles are cosmic not earthly, so Christ is God's agent and associate in the connecting work. He does God's work like his principal worker. Christ becomes a connector with humankind because of the emphasis by Paul on sin, and the polytheism Paul encounters on his mission he regards as demons. So this is a very monotheistic approach. Paul's view at the beginning and ending of letters allows for Christ's status to be included in worship, but such is not equivalent to God the Father and God the Son but through the Son to God. Also, the messianic job is still to be done, and the titles for the exalted now heavenly key worker must be incomplete.
Mark, Matthew and Luke have very much a human Jesus commissioned by God to do the special task. There is a heavenly element at times, but not pre-existent. Mark sees that Jesus sonship can give a suggestion of blasphemy, so there is the possibility here of divinity. Forgiving sins has a divine echo, but when Jesus is forgiving sins he says (that is, via Mark 2:7) God has given him this right and ability, and so in as much as Mark thinks Jesus is divine he thinks this despite the reporting of Jesus' mission coming from God, not because of it.
Matthew at Caesarea Phillipi agrees with Peter (Matthew 16:13-20), but this Son of the Living God means Messiah in this setting. Sonship is a task, not an ontological status. The title Emmanuel by Matthew is consistent with Isaiah's use, a God-bearing name. Regarding the birth, God's spirit acts through genealogy: he is of the line of David through his father, even though there is the virgin birth. Both, of course, are purely imaginary pieces of writing, trawling the Hebrew scriptures as must. For Matthew, Jesus is not God but the final way to God.
Now if the messiah is to be David's Lord as well as David's son (they argue for the latter usually, but the former is at Matthew 22: 41-45, and all three have it) then this implies becoming a heavenly Lord rather than earthly king, both being messianic.
Luke 3:38 has Adam as the son of God. A great prophet has visited and God has visited his people (Luke 7:16) run together in meaning. The prophet does the job of God visiting. The transfiguration (Luke 9:35) indicates divine appointment.
John's gospel is often regarded as most theologically complete because the development of Jesus' prophetic mission is not there - Christ starts as Christ. The Son of God is now pre-existent and divine. The divinity, however, is subordinate - before the Nicene Creed. In the beginning was the Word, and the Word was with God, and was God (John 1:1). The (Very) God we should understand as eternal when all things were made through the Word, in the beginning. Given this opening, the Jewish chosen man of God and his speech patterning is replaced with what seems to be anti-Jewish, and there is some gnosticism. Christ has moved out of Jesus' locus, and is building castles.
So there are several possible shapes. John clearly has an Arian shape - it is there already. Others, like Matthew, possibly Mark, have that potential, and Paul makes it possible. This can also be a trinitarian shape, in potential: a legitimate development. The problem is that if the source is the gospels plus Paul then the Trinity is not there.
Historically literalist Unitarians, to call them that, at the time of Priestley, said that Jesus Christ was a man, who did the work of God and was given that ability by God. He performed healing and miracles, because God made this happen. He was raised by God, exalted and rewarded. Like the synoptics, he became the Christ. Others were Arians in the sense that John's pre-existence counted for most. They were both right. As a matter of historical record in England and Wales, Arianism was not popular amongst ex-Presbyterians and even ideological Unitarians, it tended to be found most amongst Anglicans. Samuel Clarke's writings and liturgies were as influential amongst Anglicans as any; the first self-described Unitarian church minister was an Anglican priest Theophilus Lindsey who followed Clarke's views and was frustrated that other Anglican sympathisers did not follow him, and subsequently his chapel of Essex Church became part of the Presbyterian stream.
Adapted from a posting sent to surefish.co.uk on 28 September 2004
Use of: Cupitt, D. (1978), The Debate about Christ, London, SCM Press
On the Trinity in the Hebrew Bible
On the Trinity in the Christian New Testament
On Christ's Divinity in the New Testament