In terms of the Pauline Epistles and the Book of Revelations, they are genuine historical source materials... of what early First Century Christians believed in terms of doctrine and religious material.
In terms of the Gospels, again, they are primary source documents. However, in terms of how they describe the World of the First Century AD, that is a more tricky task. We can verify many things, such as Pontius Pilate as Procurator and Proconsul of Judea, amongst the Tetrarchy that ruled the region. The geography is roughly accurate, as are many of the internal dynamics of Jewish Sects. For instance, the Sadducees are correctly described as not believing in an afterlife, while the Pharisees were also correctly described as being concerned with the Law, specifically the Oral Law, but that's easy stuff. We also get roughly accurate descriptions of Publicani, or contracted tax collectors and tax farmers. The Roman Government would contract out to private individuals and groups to collect taxes on behalf of its provincial administration. They were free to collect any tax revenue they wished, so long as the necessary amount was given to the Roman Administration. This was also correctly described as deeply unpopular and prone to corruptions, as the Roman Empire did not actually oversee these directly.
However, its also difficult to verify specific events, for instance, those in the Life of Jesus Christ, or the various mentioned individuals throughout the Gospels and the Book of Acts. The reason being is that the Bible is the only one that mentions them, and we don't have a lot of alternative sources.
Generally speaking, assuming that we cut out all of the miracles and theophanies, the events described are at the very least plausible. There was a preacher, Jesus son of Joseph (Yeshua ben Yosuf), with Yeshua being one of the fourth most popular Jewish names, who was possibly related to John the Baptist (an Essene Apocalyptic Preacher who practiced baptism), who was a religious reformer and started an ad hoc, popular heretical movement in the eyes of orthodox Judaism, possibly claimed to be the messiah (as about forty others had in that time period), ran afoul of the Temple Priesthood (who were the de facto leaders of Jerusalem), possibly by cleansing the Temple, and was found guilty of heresy (by the Sanhedrin) and disturbing the peace/claiming to usurp Judea from the Roman Empire (i.e. Treason), and was executed by crucifixion. After his crucifixion, Rome probably wanted to smooth the whole thing over, and prevent a religious civil war in Judea between the Temple Elites who nominally supported Rome, and Jesus' surviving followers, so they allowed him to be buried with full funeral rites. It is not implausible that a local religious elder (Joseph of Arimathea) gave his own family tomb for Jesus to be buried within, to conform to proper Jewish Rituals. His followers probably believed that something miraculous had happened and this spread throughout Judea.
Thus, sticking to the non-miraculous content, much of what the Bible describes in terms of events are either confirmed, or at the very least plausible.
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