What is an overview of the early Church's viewpoints on Christology at the time of the Apostolic Era? What were the beliefs of the early Church regarding the nature of Jesus during the Apostolic Era? By Apostolic Era, I mean the time of the Apostles and their immediate successors who knew them personally. Do we have sufficient historical evidence to build an overview of their Christological beliefs? For instance, did Christians during the Apostolic Era believe that Jesus was 1) uppercase God, 2) lowercase god, 3) a powerful pre-existent but created being, 4) just a human or 5) any other view that I may be overlooking? Was there a particular view that was the most prevalent/popular at the time?
This has been interpreted many ways. And it is made all the more challenging by questions regarding who wrote which documents and when. For purposes of this response, I will assume the entirety of the New Testament was written by AD 100, the history in Acts is reliable, and that Polycarp represents the last surviving Christian leader who was an immediate successor to the apostles.
There is clearly much more that what known by the apostles than has been preserved in the handful of documents we have from their time.
Let's look at a few passages by decade.
The 30s
The creed preserved in 1 Corinthians 15:3-8 is held by conservative and liberal scholars alike to date to the 30s. A few key statements:

Christ died for our sins according to the scriptures; And that he was
buried, and that he rose again the third day according to the
scriptures:

Indicating a belief that Jesus died for sin and rose again--and that His work was prophesied in the Tanakh.
The 40s
I personally date the Gospel of Matthew to the 40s, but I recognize I'm in a minority position here. If we include Matthew, then already in the 40s Jesus is being called Emmanuel.
Acts 10 records a sermon by Peter with the following relevant highlights:

Jesus is Lord of all (vs. 36)
God anointed Jesus (vs. 38)
God was with Jesus (vs. 38)
God raised Jesus from the dead and Jesus appeared (vs. 40-41)
Jesus is our Judge (vs. 42)

The 50s
Here we have the bulk of Paul's teachings, including the extended sermon on the resurrection in 1 Corinthians 15, and the very high-Christology of Romans. Paul regularly refers to Jesus as Lord, and many understand Romans 9:5 to refer to Jesus as God.
1 example from 1 Cor. 15:

28 And when all things shall be subdued unto him, then shall the Son
also himself be subject unto him that put all things under him, that
God may be all in all.

This is a potent claim! All things will be subject to Christ.
The 60s
Assuming Hebrews and Colossians date to the 60s, here we have some of the highest Christology in the New Testament.
From Colossians 1:

16 For by him were all things created, that are in heaven, and that
are in earth, visible and invisible, whether they be thrones, or
dominions, or principalities, or powers: all things were created by
him, and for him:
17 And he is before all things, and by him all things consist.
18 And he is the head of the body, the church: who is the beginning,
the firstborn from the dead; that in all things he might have the
preeminence.

From Hebrews 1:

8 But unto the Son he saith, Thy throne, O God, is for ever and ever:
a sceptre of righteousness is the sceptre of thy kingdom.

Indicating, among other things, that Jesus is the creator, all things consist by him, and that His status as Deity is not in doubt.
Pre-100
Dates here are more controversial, so I'm using a range. I'll cite passages from 3 books that date to this era.

Jesus saith unto him, I am the way, the truth, and the life: no man
cometh unto the Father, but by me. (John 14:6)

(to be sure, I have no problem with the idea that Jesus said this in the 30s; this text reflects that Christians were repeating these words at this time)

That which was from the beginning, which we have heard, which we have
seen with our eyes, which we have looked upon, and our hands have
handled, of the Word of life; (1 John 1:1)


In the beginning was the Word, and the Word was with God, and the Word
was God. (John 1:1)

Since I just quoted one of the most contested passages in scripture, I'll let these verses speak for themselves =). I'll at least try not to take sides but stick to the question.
Also during this period we get clear statements against Docetism--meaning the idea that Jesus didn't really come in the flesh was something that was being said by some--and refuted by authoritative individuals. I have written on this subject here.
Early 2nd century
Ignatius wrote 7 epistles circa 107 as he was en route to Rome to be executed. In his Epistle to the Ephesians, chapter 7:

There is one Physician who is possessed both of flesh and spirit; both
made and not made; God existing in flesh; true life in death; both of
Mary and of God; first passible and then impassible — even Jesus
Christ our Lord.

Polycarp quotes the documents of the New Testament extensively, so much of his work would be a repeat of the sections above.  Two points worth making from Polycarp's epistle to the Philippians (circa AD 107):

He repeatedly refers to &quot;God and Christ&quot;
In chapter 12 he says:


But may the God and Father of our Lord Jesus Christ, and Jesus Christ
Himself, who is the Son of God, and our everlasting High Priest, build
you up

Although Polycarp lived nearly another half-century, we regrettably do not have any other surviving works by him.
Both Ignatius and Polycarp were taught by apostles. Their writings indicate respecting Jesus as God, but also acknowledging a distinction between God the Father and Jesus.
Specific questions from the OP

uppercase God &amp; 2) lowercase god: there is no distinction between majuscules and miniscules in the manuscripts of the time, so no difference would exist between &quot;God&quot; and &quot;god&quot; in these writings--this is an interpretation of the text, not an explicit repetition of the text. That Jesus is called God is found in Hebrews, John, and Ignatius, to name a few.

a powerful pre-existent but created being: The Colossians passage referred to Jesus as the beginning and the creator. Much debate could surely ensue about what the beginning means. John 1:1, John 8:58, and Hebrews 1:2 are commonly cited as evidence of Jesus' pre-mortal existence. This remains a debate in New Testament interpretation to this day, but at the very least we can safely say that the texts used in these debates were in circulation during the apostolic era.

just a human: I find no references to support this view, except on the lips of Jesus' enemies.


Theological development
If the Gospel of John reliably preserves the teachings of Jesus, then the idea of theological development transforming Christian thought between the 30's and the 90's is unsound. The Christology of the apostles themselves stayed right around the same place from ~Pentecost until the end of the century.
If the Gospel of John is a late, unreliable document (this is not my view), then at the very least, we've got full on high Christology within a few years of AD 60, well within the lifetimes of multiple apostles and numerous eyewitnesses.
Once upon a time I created a video pointing out the flaws in trying to introduce patterns of changing theology in the New Testament. That video can be found here.
My own studied view with respect to Christology &amp; chronology is that the highest Christology in the New Testament is fully consistent with what the apostles believed in the early 30s; they didn't teach the most profound doctrines until they'd laid a &quot;milk before meat&quot; foundation, which is why so many early documents do not contain some of the more potent teachings by Jesus about who He was. I have a post on SE-Hermeneutics discussing this specifically with respect to the Gospel of John.
Some wish to say New Testament theology shows a sequence of development between the 30s and the 90s--I disagree. I believe major changes in Christian understanding of theology happened:

Between Jesus' baptism and Pentecost
After the apostles were gone

Concluding thoughts
The writings of the apostles and their immediate successors suggest that from very early on, Christianity was plagued with diverse doctrines. I see in the teachings of the apostles themselves, however, that Jesus was Divine and that He was distinct from the Father. Both of those principles have been reworked many times over the millennia to produce a variety of theologies that were not taught by the apostles.
What about the later creeds? From Harper's Bible Dictionary:

the formal doctrine of the Trinity as it was defined by the great
church councils of the fourth and fifth centuries is not to be found
in the [New Testament] (see here p. 1099)

So the creeds aren't there in the first century, but the most significant passages that would be used to support many theologies over the years (which surely is not what the apostles wanted) were all there within the first century.
This is a difficult topic upon which to give an even-keel overview. My own beliefs are described here.