What view of eschatology did the early church believe? I have recently been studying eschatology and have been looking at the main views of eschatology.  

So far, I have found four (I apologize in advance if I have misrepresented your view.  I would appreciate any corrections, but that is beyond the scope of this question.): 


Amillenialism: Jesus' Ascension began the "Church Age/Millennial Kingdom"; this age will be one of peace but will eventually turn into a period of tribulation against the Christians.  Armageddon, the Rapture, Jesus' Return, and the White Throne will end this age and usher in eternity.  
Post-Millennialism: The period between Jesus' Ascension and the Destruction of Jerusalem will be the Tribulation.  The "Church Age" began in A.D. 70; at some point, the earth will develop a "Christian" culture ushering in a spiritual millennium of peace.  The Great Rebellion, the Rapture, Jesus' Return, and the White Throne Pit will end the millennium and begin eternity.  
Historic Pre-Millennialism:  Jesus' Ascension began the "Church Age"; this age will be one of peace but will eventually turn into a period of tribulation against the Christians.  Armageddon, the Rapture, Jesus' Return, and the Bottomless Pit will end this age and will begin Jesus' physical reign on earth of exactly 1000 years.  The reign will end with the Great Rebellion and the White Throne to usher in eternity.  
Dispensational Pre-Millennialism: Jesus' Ascension began the "Church Age"; this age will end unexpectedly with the Rapture.  A literal tribulation of 7 years will begin on earth.  Armageddon, Jesus' Return, and the Bottomless Pit will end the tribulation, and Jesus will begin his physical reign on earth of exactly 1000 years.  The reign will end with the Great Rebellion and the White Throne to usher in eternity.  


What view did the early church have?  Did they hold on to one of these views or did they hold on to a view that I have not listed?  

I appreciate the help.
This is a difficult question to answer, because the early church did not approach the question in the same way that many people do today.  The earliest fathers expressed their belief in various eschatological views, like the immortality of souls, the return of Christ, the resurrection of God's people, and a general judgment, but they did not develop systematic understandings of eschatological doctrine.  Louis Berkhof summarizes the situation this way:

In the very first period the Church was perfectly conscious of the separate elements of the Christian hope [...] but these elements were simply seen as so many separate parts of the future hope, and were not yet dogmatically construed. Though the various elements were quite well understood, their interrelation was not yet clearly seen. (Systematic Theology, 6.1.B)

Thus, the best we are going to be able to do is gain a high-level understanding of what eschatological aspects the fathers accepted, and maybe the order in which such things would happen.
Millennium
The first big question is, what did the church fathers believe about the millennium of Revelation 20?  That in itself is a big question, but I'll briefly describe the two major views: Chiliasm (post-tribulation premillennialism) and amillennialism.
Some of the earliest Christian writers appear to have believed in a thousand year earthly reign of Christ.  Fragments from Papias (d. ~163) say that he believed:

that there will be a millennium after the resurrection from the dead, when the personal reign of Christ will be established on this earth. (VI)

Several other major church fathers appear to have been of the same opinion, including Irenaeus (d. 202).  A later writer, Eusebius (d. 340), critiques them but gives us some insight as to the extent of these beliefs:


To these [writings] belong [Papias's] statement that there will be a period of some thousand years after the resurrection of the dead, and that the kingdom of Christ will be set up in material form on this very earth. I suppose he got these ideas through a misunderstanding of the apostolic accounts, not perceiving that the things said by them were spoken mystically in figures.

For he appears to have been of very limited understanding, as one can see from his discourses. But it was due to him that so many of the Church Fathers after him adopted a like opinion, urging in their own support the antiquity of the man; as for instance Irenæus and any one else that may have proclaimed similar views. (Ecc. History, 3.39)



As the quote from Eusebius suggests, after the first couple centuries, Chiliasm was largely superseded by amillennialism.  Clement of Alexandria (d. 215), Origen (d. 254), and especially Augustine (d. 430) contributed to establishing amillennialism as the standard view of the church.  Augustine believed that the millennium of Revelation 20 referred to the church age:

the whole time which this book embraces,—that is, from the first coming of Christ to the end of the world, when He shall come the second time,— [...] during this interval, which goes by the name of a thousand years. (City of God, 20.8)

Tribulation
Among those who believed in an earthly millennial reign, the fathers believed that the church would undergo the tribulation.  Hippolytus (see his Treatise on Christ and Antichrist, 64) and Irenaeus are two good examples, the latter of which wrote:

And therefore, when in the end the Church shall be suddenly caught up from this, it is said, “There shall be tribulation such as has not been since the beginning, neither shall be.” For this is the last contest of the righteous, in which, when they overcome they are crowned with incorruption. (Against Heresies, 5.29)

Preterism
Preterism is not one of the views you listed, probably because you are focusing on futurist understandings of the eschatological passages in the Bible.  However, there is evidence that at least some early Christians understood Jesus's predictions in the Olivet discourse (Matthew 24, Mark 13, and Luke 21) as fulfilled in the AD 70 fall of Jerusalem.  Eusebius discusses this at length, arguing that the tribulation, death, and famine described by Jesus had already happened.  For example:

[Josephus] also shews plainly the fulfilment of the prediction of our Saviour [...] for he has put it on record, how the women roasted their children by the fire and ate them, on account of the pressure of the famine which prevailed in the city. (On the Theophania, 4.18–20)

In the interest of brevity, I won't analyze other writings that proponents of preterism argue are evidence of early support for their viewpoint.  Suffice to say that an understanding of early church eschatology requires realizing that a futurist interpretation was not always applied to passages commonly considered to be unfulfilled prophecy today.
Summary
We need to avoid the temptation of attempting to squeeze the views of the church fathers into our convenient little boxes.  They did not approach eschatology in the same systematic way that many do today.  Furthermore, many of the earliest writings have been lost, making an analysis like this even more challenging.
For more information, I'd recommend Gregg Allison's Historical Theology.