At the time of Jesus, the Pharisees were teaching the following about what happens to a person after death (source: the first century Jewish historian, Josephus, in his discourse to the Greeks regarding Hades)
For the sake of accuracy, it should be pointed out that Josephus did not write this. This is a mistaken attribution that arose in late antiquity. It is now generally thought to have been written by Hippolytus in the third century AD. The notion of a blessed afterlife in Abraham's bosom however appears in the Testament of Abraham.
Josephus does present information on the eschatological beliefs of the Essenes, Pharisees, and Sadducees twice in Bellum Judaicum (2.153-165) and in Antiquitates (18.14-18). The similarity between the two passages, and their literary position in the text, suggests that Josephus is using an earlier source. The same information is presented in a closely parallel way by Hippolytus (Haereses 9.26-29), and it is generally thought that Hippolytus was using the same source that Josephus used, and more faithfully preserved the original wording of the source. There is much evidence that Josephus' main source for this part of his narrative in Antiquitates was Nicolaus of Damascus (first century BC), and so the latter was likely the direct source for the descriptions given by both authors.
With regard to the Essenes, we read that the Essenes teach that "souls persevere, forever immortal ... becoming entangled in bodies as in prisons" (Josephus, B.J.), and that "they acknowledge that the flesh will rise again and that it will be immortal, in the same manner as the soul is already immortal. And they maintain that the soul, when separated in the present life, departs into the one place, which is well ventilated and lightsome, where they say it rests until judgment. And this locality the Greeks were acquainted with by hearsay and call it the 'Isles of the Blessed' " (Hippolytus, H.). Josephus adds that this is an "abode beyond the sea" where "the eternally gentle west wind refreshes it as it blows in from the ocean," whereas the wicked are "set apart in a dark and wintry recess filled with never ceasing punishments". This description is strongly Hellenized, drawing on Platonic and traditional Greek ideas, but it is very close to Essene ideas found in Enochic literature and in the Dead Sea Scrolls. The Essenes had their own notion of the immortality of the soul and the Book of Watchers (third century BC) describes the abode of the spirits of the righteous and wicked in strongly similar terms: the righteous reside beyond the great sea beyond where the sun sets in the west and are given a spring of water with light on it, whereas the wicked are separated and set apart from them in their own chambers (1 Enoch 22). This notion is clearly reflected in the statements by Josephus and Hippolytus, and it clearly is related to the conceptualization of the abode of the dead in the parable of Rich Man and Lazarus. It should be noted that the rather geographical depiction of Sheol in the Book of Watchers was superseded by more cosmic conceptions in later sources, such as 4 Ezra (late first century AD), which has the righteous and the wicked in separate locales in Hades (4:35-42, 7:80-99), the wicked going directly to punishment than habitation. There however was also the idea that the storehouse for the post-mortem righteous was located in heaven (as it is in Revelation 6:9-11), and this idea was apparently common to the Pharisees (cf. the teaching of R. Eliezer b. Hyrcanus in b. Shabbat 152b).
With regard to the Pharisees, we read in Hippolytus that they "acknowledge that there is a resurrection of flesh and that the soul is immortal, and that there will be a judgment and conflagration, and that the righteous will be imperishable, but that the wicked will be punished forever in unquenchable fire" (H.), and the same idea is presented by Josephus who says that the Pharisees believe that "souls have immortal power, and there are punishments and rewards under the earth, for those whose devotion in life has been either vice or virture. For the latter there is appointed an eternal imprisonment" (Ant.), such that "the souls of the wicked are chastised by everlasting punishment" (B.J.), whereas for the former there is appointed "an easy passage to revivification" (Ant.). The eschatology of the Society is rather close instead to that of the Sadducees, who did not believe in the resurrection. According to Josephus, "their teaching is that souls perish together with bodies" (Ant.), and they do away with the idea of "the survival of the soul and punishments down in Hades and rewards" (B.J.), and as Hippolytus represents his source, the Sadducees "deny that there is a resurrection, not only of the flesh but also they suppose that the soul does not endure. It is only the life and it is on account of this that man has been created .... After death one expects to suffer nothing, either bad or good, for there will be a dissolution of both soul and body and man passes into non-existence, similarly also with the material of the animal creation" (H.).
As to whether earliest Christianity drew more from either of these different parties of Judaism, I agree with Boccaccini that the Jesus movement is closest to Essenism than to the other groups. It stands very close to the kind of Essenism responsible for the Book of Parables, which was a possible influence on the synoptic gospels (especially wrt eschatology). The heavy Enochic influence in Jude (attributed to a "brother of Jesus") is also one indicator of this, as is the description of John the Baptist in the synoptic gospels and in Josephus. The kinship of the parable of Rich Man and Lazarus with the Enochic conception of Sheol is thus consistent with this. Note too that this parable is original to Luke and is absent in the other gospels, and parallels between Luke and the Epistle of Enoch (particularly pertaining to the theme of the rich and the poor) have been noted by Nickelsburg and other specialists of Second Temple Jewish literature. It is clear that the parable is not critical of the eschatology it espouses, nor uses it purely in a figurative sense, but that the eschatology is presupposed in order to describe the rich as having their comeuppance. The moral it presents to the rich is that they must change their ways or they will have their roles reversed after death. This illustrates the aphorism that the "first shall become last and the last shall become first" (Mark 10:31, Matthew 19:30, 20:16, Luke 13:30). JW eschatology voids this moral because both the rich man and Lazarus would have equal opportunities in the resurrection recreation, so it doesn't matter how good or poor a life one leads in this life .... as long as one dies before Armageddon.