This is what Josephus has to say in Antiquities of the Jews Book 18 Chapter 1.
2. The Jews had, for a great while, had three sects of philosophy peculiar to themselves. The sect of the Essens; and the sect of the Sadducees; and the third sort of opinions was that of those called Pharisees. Of which sects although I have already spoken in the second book of the Jewish war;1 yet will I a little touch upon them now.
3. Now for the Pharisees, they live meanly, and despise delicacies in diet; and they follow the contract of reason: and what that prescribes to them as good for them they do: and they think they ought earnestly to strive to observe reason’s dictates for practice. They also pay a respect to such as are in years: nor are they so bold as to contradict them in any thing which they have introduced. And when they determine that all things are done by fate,2 they do not take away the freedom from men of acting as they think fit: since their notion is, that it hath pleased God to make a temperament; whereby what he wills is done; but so that the will of man can act virtuously or viciously. They also believe that souls have an immortal vigour in them: and that under the earth there will be rewards, or punishments; according as they have lived virtuously or viciously in this life: and the latter are to be detained in an everlasting prison; but that the former shall have power to revive and live again. On account of which doctrines they are able greatly to persuade the body of the people: and whatsoever they do about divine worship, prayers, and sacrifices, they perform them according to their direction. Insomuch, that the cities give great attestations to them, on account of their intire virtuous conduct, both in the actions of their lives, and their discourses also.
4. But the doctrine of the Sadducees is this; that souls die with the bodies. Nor do they regard the observation of any thing besides what the law enjoins them. For they think it an instance of virtue to dispute with those teachers of philosophy whom they frequent. But this doctrine is received but by a few: yet by those still of the greatest dignity. But they are able to do almost nothing of themselves. For when they become magistrates; as they are unwillingly and by force sometimes obliged to be; they addict themselves to the notions of the Pharisees: because the multitude would not otherwise bear them.
5. The doctrine of the Essens is this; that all things are best ascribed to God. They teach the immortality of souls: and esteem that the rewards of righteousness are to be earnestly striven for. And when they send what they have dedicated to God into the temple, they do not offer sacrifices: (3) because they have more pure lustrations of their own. On which account they are excluded from the common court of the temple: but offer their sacrifices themselves. Yet is their course of life better than that of other men; and they intirely addict themselves to husbandry. It also deserves our admiration, how much they exceed all other men that addict themselves to virtue, and this in righteousness: and indeed to such a degree, that as it hath never appeared among any other men, neither Greeks nor Barbarians, no not for a little time: so hath it endured a long while among them. This is demonstrated by that institution of theirs, which will not suffer any thing to hinder them from having all things in common: so that a rich man enjoys no more of his own wealth, than he who hath nothing at all. There are about four thousand men that live in this way: and neither marry wives, nor are desirous to keep servants: as thinking the latter tempts men to be unjust; and the former gives the handle to domestick quarrels. But as they live by themselves, they minister one to another. They also appoint certain stewards to receive the incomes of their revenues, and of the fruits of the ground; such as are good men, and priests: who are to get their corn, and their food ready for them. They none of them differ from others of the Essens in their way of living: but do the most resemble those Dacæ, who are called Polistæ. [Dwellers in cities.] (4)
6. But of the fourth sect of Jewish philosophy, Judas the Galilean was the author. These men agree in all other things with the Pharisaick notions; but they have an inviolable attachment to liberty; and say that God is to be their only ruler and lord. They also do not value dying any kinds of death; nor indeed do they heed the deaths of their relations and friends: nor can any such fear make them call any man lord. And since this immoveable resolution of theirs is well known to a great many, I shall speak no farther about that matter. Nor am I afraid that any thing I have said of them should be disbelieved: but rather fear that what I have said is beneath the resolution they shew when they undergo pain. And it was in Gessius Florus’s time that the nation began to grow mad with this distemper; who was our procurator; and who occasioned the Jews to go wild with it, by the abuse of his authority; and to make them revolt from the Romans. And these are the sects of Jewish philosophy.
Based on the Metaphysics it's clear that the sect of Judaism to which the Early Christians at least nominally belonged was basically the Pharisees. That can be difficult for a moderner to wrap their head around given how much the word "Pharisee" is colloquially treated as synonymous with being the "Bad Guys" of the Gospels.
Often people who clearly qualify as Christians but exist outside the mainstream will simply refer to what they oppose as "Christianity", I personally try not to do that even though I have greater disagreement with the mainstream Church then some who do, but it is a thing.
Josephus also tells us here that most of the common people were basically with the Pharisees, so those mass crowds of people Jesus attracted must have been made up of lots of Pharisees. And then Josephus suggests a lot of people in positions of power were really Sadducees merely pretending to follow the popular religion.
There are hints in The Gospel narrative itself that Jesus' criticisms of the Pharisees are really criticisms from within directed at their leadership.
In the first three verses of Matthew 23 Jesus tells us two things about the leaders of the Pharisees. The seat they sit in makes them legitimate heirs of Moses, this to me confirms that the Sanhedrin of the Greco-Roman period as an institution does have unbroken continuity with the Council of Seventy Elders ordained in Numbers 11:16-25.
The other appears to be that what they preach is correct, they simply don't practice what they preach. Other things Jesus says about them may seem inconsistent with that, seem absolutely about what they teach. But I think "from a certain point of view" how you practice what you preach can include how you teach it and interpret it. The point is Jesus couldn't have said that if He disagreed with the core definition of being a Pharisee.
Luke 7:36-50 features a Pharisee named Simon who Jesus is on pretty good terms with.
In Acts 23:6 Paul identifies himself as still a Pharisee on simply the grounds that He believes in The Resurrection of The Dead. So likewise all of Christianity can claim the same.
According to the timeline that can be inferred from The Talmud, Shammai was head of the Sanhedrin from about 20-30 AD. Some have observed similarities between the teachings of Jesus and Hillel the Elder, the head of the School that Shammai opposed. This particular internal disagreement within the Pharisees doesn't come up in Josephus, possibly because in his time the Shammai school was already mostly defunct. But the time period I and many others place the ministry of Jesus is at the height of Shammai's influence, so the Pharisees who are the bad guys of the Gospels could be mainly him and his followers. I do think certain people online overstate the similarities between Jesus teachings and Hillel's to suit various misguided agendas of their own. But it's interesting because modern Rabbinic Judaism also descends not only from the Pharisees but specifically Hillel's school. Perhaps Shammai should have filled the role of the made up Zerah (played by Ian Holm) in the 70s Jesus of Nazareth miniseries.
However even in Josephus's brief description of the Pharisees there is at least one apparent disagreement with The New Testament view of The Resurrection, and that's how it seems ONLY the "Righteous" will be Resurrected. 1 Corinthians 15, Acts 24:15, Revelation 20 and Jesus in John 5:28-29 are all clear that everyone no exceptions will rise again., and The Hebrew Bible agrees with the NT on this in Daniel 12. Now as a proponent of Universal Salvation I disagree with most mainstream Christians on exactly what it means that the unjust will face "Judgment" after their Resurrection, but we do all still agree that they will also rise again to a literal bodily Resurrection.
And that last point is key to why I wanted to discus the Doctrine of the Resurrection in the context of 1st Century Judaism. Some people try really hard to abuse certain details of 1 Corinthians 15 and 2 Corinthians 5 to suggest Paul and other NT writers must mean by "Resurrection" something that is actually functionally the same as what either the Essenes (we live forever as immortal souls without a body) or Sadducees (no real after life at all) believed. However we see here that people who believed those kinds of things in first century Judaism didn't use the language of Resurrection, so it's silly to think Paul or Peter or Jesus would if that's what they meant.
Another interesting observation I can make from Josephus's description is how there was a familiar debate about Human Free Will vs Divine Sovereignty. With the Essenes being like Augustine and the Calvinists, while the Sadducees were more like Pelegius or the Arminians. The Pharisees however have a more nuanced take on that tension that again I feel is closer to what The New Testament is actually saying, but could also be compared to the Stoic position on Free Will vs Fate in Greek Philosophy. I also feel like the Sadducees are functionally Deists, what we today call Deism began in Greek Philosophy with Aristotle and then the Epicureans.
Many people want to connect the Essenes to the origins of Christianity based on their practicing a voluntary communalism similar to the Early Church in Acts. But they did it for a different reason, they had inherited a Pythagorean notion of the Immortality of The Soul, and indeed Classical Pagan Pythagoreans also practiced a sort of Voluntary Communalism, but for both it was about viewing the physical world as a Prison they seek liberation from. Early Christians lived this way to be a light within the world and salt of the earth. The Early Christians were true Communists, the Pythagoreans were more like Strasserists or NazBols, they were in bed with totalitarian governments in Samos and Crotone, and likewise I have argued that those Josephus called Essenes were those Matthew 22 called Herodians. Philo's description of the Essenes also repeats that they had the support of many "Great Kings". I've also talked about the Pythagorean role in the origins of Puritanical Sexual Morality, and the Essenes seem to have been the same way on that too, as well as their Misogyny, I think the Essenes were basically Herod's Proud Boys. The Zealots were the Revolutionary Anarchists, and they were also originally a sect of the Pharisees.
Update: Of course much Confusion about the Essenes exists because of how they are conflated with the Dead Sea Scrolls. Many have questioned that connection for reasons that have little to do with why I'm skeptical of it.
I partly reject it, I don't think the Scrolls all have a common origin. Even if they did all come from that one settlement called Qumran, maybe the assumption everyone living there was all of the same sect is wrong. Some Scrolls do seem fairly consistent with how Josephus described the Essenes, but other Scrolls mention the Resurrection, and also clearly have an interest in Eschatology and The Messiah.
Roman A. Montero in All Things In Common says the Pythagoreans weren't like the Essenes or Early Christians because they weren't Messianic or Apocalyptic. But the thing is from what Josephus tells us, Eschatology was inherently the purview of the Pharisees, people with Essene or Sadducee views on the After Life would be just as uninterested in the Future as most Pagan Greeks were. He also mentions how the Pythagoreans were a purely upper class phenomena, and again based on the Herodian connection I think the real Essenes were too. It's possible at Qumran the Essenes were the Bourgeoisie who owned the place while the Pharisees were the Proletariat.
Update: "Everlasting Prison".
The "everlasting prison" in the above translation of Josephus's description of the After Life view of the Pharisees might in some other translations read "eternal prison". In this case Eternal/Everlasting is Aidios which in a real sense does mean that, not Aionios which never actually means that.
Some of my Universal Salvation allies make much out of the Pharisees here using different language then Jesus who used Aionios and not that particular word for "prison" either, saying Jesus would have used the same word if He also meant a punishment with no end. But I feel we overstate our case on that one a bit.
First of all Jesus was not speaking in Greek, and what ever main doctrinal statements the Pharisees had that Josephus got this from probably weren't in Greek either, they were either Hebrew or Aramaic. I am also with those who believe Matthew's Gospel was originally written in one of those languages not Greek. The possibility that Josephus and the New Testament are sometimes translating the same Semitic expression into Greek differently can't be ruled out.
However even the Greek words in question can have nuance to how they are used. Jude used "Aidios chains" to describe an imprisonment that is clearly defined as having an end. And in my view those Angels are not Supernatural Angels but those who were swallowed up by the earth with Korah and Dathan. So the Prison in the Pharisees eschatology could be Aidios in the same way Jude's chains are.
Maybe my prior assumption that Josephus or the Pharisees he got that from were absolutely precluding the Unrighteous from future Resurrection was mistaken. Maybe the contrasting language there is like those Bible Verses that seemingly contrast "Life" and "Judgment" at the Resurrection. The Pharisees Jesus was most often in conflict with certainly seem like the kinds of people who wouldn't like Universal Salvation. But I doubt the very idea was inherently unheard of in Pharisee circles.
In Josephus's description of the Zealots when he says they refuse to "call any man lord" for God is their only Lord, I do think that is a different Greek translation of the same sentiment Jesus expressed in Matthew 23:8-10, one says "Master" the other says "Lord" but the gist of meaning is the same.
Usually when someone suggests Jesus and the Early Christians were Zealots it goes hand in hand with saying the Pacifist parts of His teachings were a later Romanized white washing. However I have come to see the Zealot movement as like the Anabaptists of the 16th Century and Secular Anarchists of modern history (and Petr Chelčický could be considered the Pacifist Taborite), they included Violent Rebels like Thomas Muntzer, absolute Pacifist Separatists like those the Mennonites, Hutterites and Amish descend from, and many gradients in-between. With the reputation of the violent rebels often used to justify not believing the pacifists when they claim to be non-violent.
