@BishopAs for the legitimacy of New Testament writings, we have the fortune of the events being so recent (less than two thousand years ago) that we have an incredible deal of information regarding the development of early Christianity and the way that the books were distributed. One of the greatest factors is that these events are not recorded by historians hundreds or even thousands of years after the original events occurred (I'll point to Alexander the Great, the earliest biography of whose was written over four hundred years after his death). In contrast, the events depicted in the New Testament were recorded within thirty years of the death of Jesus (which, in terms of ancient historical records, is nothing). (I'd also like to add that the reason they were written as late as they were instead of immediately after is because the Jewish culture was very orally-oriented, meaning that for the most part, information was passed by word of mouth and information was only documented when it was to be preserved—though the Jews took very good care in ensuring accuracy when creating these records. They were likely written near the end of the lives of the original authors who decided that they would write down their sermons, experience, or other information. They also did not collaborate in their writings, based on style, information, and date of the original creation of the documents.) While the New Testament is much more moralistic than it was historical (in contrast to the Old Testament, which is much more a collection of history that happens to shine light on the actions and nature of God), it has a great deal of history involved and several sociopolitical factors at play in the origins of its spread. The primary goal of the New Testament was not to preserve history or even religious law, but rather to show that the Jewish covenant (The Law of Moses) was now overwritten by the law of Christ, shifting the focus of the relationship with God from a traditional, action-oriented approach to one based on intention and personal interaction with God. So because of this, historians have less to argue about in terms of historical legitimacy, because several books (like many of Paul's letters) are written with religious instruction and little to no historical information (other than perhaps something along the lines of "I am writing from Galatia" or "I traveled to Damascus," which historians have no real reason to question).
Like the court of law, when historians seek to show that a document has the potential to be false, they often look for intention on the part of the author to falsify information. Perhaps this is where the misconception that the Bible could have been written for political or religious power, but unfortunately, the fact of the matter is that early Christians were very much persecuted for their beliefs, and this is well documented in extrabiblical ancient writings. In fact, the original apostles and early Christians would only have to reject their writings as falsehoods in order to escape persecution, but they held onto their statements throughout both torture and execution (which the Romans were particularly skilled at). Historians recognize that they died for their beliefs and reject the notion that they would have allowed themselves to be tortured and killed to perpetuate what they knew to be falsehood. For this reason, we know that the original apostles and early Church very much believed in what they taught. The question at that point is no longer "are they lying about their experiences," but rather "can the information presented in these documents be trusted as historically accurate?"
Because of the spread of the writings of the apostles after the events were recorded, we can track how they spread, when, and where rather easily. Because we know of both the culture and the time period of those who joined Christianity of that age, we don't have reason to believe that the original documents are forgeries or have false authorship, because the documents would not be accepted into early Christianity if they had. In fact, we have several case studies where early authors who
did seek to gain religious authority attempted to introduce forged documents such as the Gnostic texts, which were rejected by the early Church due to the rigorous standards and methods used to determine whether the document in question was legitimate. Based on these facts, we can conclude that the documents in the New Testament are original and that the authors are who they claim to be (though nobody is aware of who wrote the book of Hebrews). Then the question becomes whether or not these accounts have been corrupted (and there were many attempts to corrupt the original New Testament books throughout the history of the early Church). However, due to the aforementioned documentation procedures by the Jewish people, it has been found that the original text of the New Testament has been preserve with 99.5 percent accuracy, with the remaining half a percent being minor variations in the spellings of names, potentially due to regional differences. However, there has been zero change in meaning or even wording in the original documents; we know this because we have found more copies of early New Testament manuscripts than any other ancient document (with over 5,800 complete or fragmented Greek manuscripts, 10,000 Latin manuscripts and 9,300 manuscripts in various other ancient languages including Syriac, Slavic, Gothic, Ethiopic, Coptic and Armenian, according to New Testament historian Ehrman, I believe).
At this point, we know that the New Testament manuscripts are authentic, unchanged, by eyewitnesses, and believed to be true by both the authors and the early Church. To outline further evidence that historians examine in order to determine the legitimacy of writings, we can turn to the same factors we looked at before: embarrassment and hurting one's own case. If the disciples wanted religious power, they would have written off a majority of their mistakes and errors when creating the texts. However, the four gospels (Matthew, Mark, Luke, and John) as well as other New Testament books are filled with mistakes made by the apostles (and contain very little of what they actually did right). It showed them in disbelief, in lack of faith, in anger, and in other unflattering positions that would not have been brought up had they been manufacturing their experiences. In addition, the disciples also hurt their own cause by attacking their own reputations with their improper behavior, but, more importantly, through the eyewitnesses after their claims of a resurrection. They claimed that the first people who had seen the tomb of Jesus empty were two women, and according to ancient Jewish tradition, women are unreliable sources of information. There is no case in which the authors of the New Testament would have cited women as the eyewitnesses of the empty tomb and the first citing of Jesus after his death, unless they were recounting legitimate acts that had taken place (to clarify: that this account is legitimate, but this does not prove that Jesus rose from the dead in and of itself). The next most impactful evidence is that the authors of the New Testament named specific people as additional sources for some of their accounts. In this culture and style of writing, when a source is named, this means that the individual cited is still alive, well known, and can be asked to testify toward the accuracy of the claims presented. If the accounts of the New Testament had been illegitimate, there would have been disputes and qualms with naming people who did not exist, people who had died, or people who did not truly back up their claim, the writings would have been rejected and the belief discarded. This means that, if nothing else, the writings of the New Testament are historically accurate and are accepted by many historians to be accurate depictions of the world and acts of the Jewish people of that time with several external sources to support the accounts.
The only real area where legitimacy is significantly challenged is in the depictions of miracles in both the Old and New Testament, but the problem that many historians face is why the historical accounts have so much evidence to support them when (on an individual basis), the historian may not believe in miracles. So the solution for many of them is to create a naturalistic explanation for many of the events in the Bible, which the people of the time attributed to God out of ignorance. While some absolutely can be patterned to follow this trend (as Christian and Jewish theology both assert that God often utilizes both natural and supernatural occurrences to administer his will—see: the destruction of Sodom and Gomorrah, likely by volcano), there are far too many claims that do not have any natural analogue to be able to reduce to ad hoc explanations for natural events.
If you have any questions or disagreements, I'd be happy to address those, or I could also discuss the proposed solutions/countersolutions to this issue of historical accuracy/miraculous nature misalignment.