I personally think Jesus was probably based on a person that really existed, but I think how much we might be able to say about him historically is questionable on almost every level.
1- There’s not any non-Christian historical evidence for Jesus, and Jewish historians of the time he was supposed to have lived do not mention him in any known text. Jesus isn’t credited with writing anything himself and there are no contemporary accounts.
2- No one knows who wrote the Gospels (the traditional names were assigned later). They were written anywhere from 30-70+ years after the supposed death of Jesus and they were not written by eye-witnesses. Mark is considered by most scholars as being the earliest and John the last.
3- It is obvious that some of the stories relayed in the Gospels were fabricated because they do not match with the available historical evidence (this is most especially true regarding the birth stories — as just one example: Romans conducting a census where people had to go to the birthplace of their ancestors to register is not historical or even rational). Many scholars consider the whole birth account to be a later invention. The Gospels also disagree on key details (e.g.: did Jesus and his family flee to Egypt for a period of time or not?). I could write a book about all the problems with the Gospels (without even considering the supposed miracles), but I’ll pass over it for now.
4- There are only about 8 books in the NT which were probably written by the person claiming to have written them, most of the rest are very highly debatable or are considered obvious forgeries. Someone named John (a common name) wrote Revelations, which is not a book we can use for history (considering it is “vision” of the future). The other 7 books were all written by Paul. These are really the earliest accounts we have of an “historical” Jesus, but they were written beginning roughly 15 years after Jesus was supposed to have died by a person that never met Jesus while he was supposed to have lived (he only claims he saw him in a vision). In his writings, Paul doesn’t reveal any knowledge of Jesus’ birth, or much of his life or his ministry, so he isn’t a good source for an historical Jesus. Paul does claim to have met with some of Jesus’ disciples, but had serious disagreements with them.
5- There were many other “books” about Jesus (most – if not all – written even later than the Gospels), but none of them were included in the Bible (so even the “Christians” that ended up dominating the movement rejected them as spurious, and we can probably reject them as not having much historical value).
6- The first scraps we have of the “books” of the Bible are from decades after they were written, with the first complete books coming centuries after that. There are more discrepancies between the oldest versions of these books than there are words in the New Testament. Many discrepancies are the result of obvious copying errors, but some are more significant. It is also evident that certain passages were added on later (since they don’t appear in the oldest versions). If we can see things being added after the oldest copies we have, we might assume that some things might have been added before the oldest copies we have as well.
Considering that many of these books were written decades after the fact to begin with, and were probably passed down orally before they were written down, you might wonder how many changes they went through before they were written down (have you ever played telephone?).
7- Consider two things about the people passing them down orally in the beginning: they may not have been well educated and they might have had an agenda (they were probably not objective). Also consider the people writing them down later may have been attempting to “sell” others (for example: there is a lot of evidence that events were added to the account to prove what they thought was a prophecy — the evidence for this is that they made mistakes trying).
8- Most of the “key” elements of Jesus’ life found in the Bible match elements of at least 16 other mythological god-men that predate Jesus. This suggests the very real possibility that these elements were copied (imitated) and might be considered to be highly questionable historically.
9- The stories all include accounts of miracles and events that defy known laws of physics, biology, cosmology, etc., which would be considered mythological coming from almost any other source.
Someone like a Julius Caesar can be established to have existed with much greater reliability. Even someone like Socrates can be better established (there were contemporary accounts by people who knew him, his student Plato wrote about him, there weren’t any claims of him violating the laws of nature, etc.).