I afraid there is nearly no objectively 'accurate' either contemporary or later descriptions of the Vikings, as is often the case with the distant past more than a millennium ago. We must be very careful to analyze virtually all of the texts, regardless of the contemporary or later ones, when we try to re-construct something from what the scribes wrote on the Vikings since nearly any single author neither understand or write the very wide range of various activities of the Norsemen during the Viking Age, let aside whether they intentionally tried to twist facts or not.
The credibility of several contemporary chroniclers in the 9th century British Isles as well as Frankish polities has been especially vehemently debated among the historians for more than half a century since Peter Hayes Sawyer's pioneering work, the Age of the Vikings (1st ed. 1962, 2nd ed. 1971) had been published.
Anyway, the following primary texts and source books are my recommendations as at least partly useful for approaching their expansion into North-Western Eurasia:
The editors have just updated the most convenient and popular primary text collection, the Viking Age: A Reader, intended for the use in the undergraduate classroom in Anglophone countries, into its third edition, though many of the included texts must be taken with a grain of salt.
The first of the texts in this source book, Ohthere (Ottar in Old Norse)'s voyage across the Northern Seas and his livelihood in his homestead in Northern Norway, now extant in the additional section of Old English 'translation' of Orosius is the text I would also recommend first and foremost. The scribe of OE Orosius, commissioned by King Alfred of Wessex (d. 899) who is also famous for his struggle with the Viking invaders, inquired this Norwegian visitor (aristocrat-trader), together with another indigenous traveling trader (probably) Wulfstan, for complementing the geography of Northern Europe to Latin original.
On the other hand, several 10th century Arab geographers or diplomats record the customs of Rus people those who are active as fur and slave traders in the river networks of now Russia, though most of us (including myself) can access to their text only as a modern English translations and the accurate rendering of the original into such translations is sometimes very difficult. These Rus' people appeared in their are usually identified with Norsemen those who expanded into Eastward, and the most famous text of this kind is the travel account of Ibn Fādlan, an Abbasid envoy from Baghdad in the beginning of the 920s (Lunde & Stone 2012).
As for the Norse expansion and settlement into the North Atlantic, the oldest historical account from medieval Iceland, the Book of the Icelanders (Íslendingabók) (link to pdf of good English translation), written before 1133, should be firstly consulted.
I suppose that these three sources reflect not so comprehensive but relatively 'accurate' aspect of the activities of the Norsemen in the last centuries of the first millennium CE.
......OK, you want rather the raiding in Western Europe?
My favorite is Irish scholar Dicuil's observation in his Liber de mensura orbis terrae on Northmen's activities in the Northern fringe of the British Isles as well as in the North Atlantic Isles, seemingly completed in about 825. Ohthere, Ibn Fādlan, and this Dicuil are also the three text cited in the latest introductory book of the Vikings by Nordeide and Edwards (Nordeide & Edwards 2019).
Norsemen in the Viking Age Scandinavia themselves, those who were generally believed to have lived in oral society prior to the reception of latin alphabets with Christianity, in fact left some written records in form of Runic stone inscriptions. These inscriptions were primarily the commemoration of the dead person, commissioned by wealthy relatives of the diseased, and sometimes mention distant place name where the diseased met their end, either as a member of the Viking ship band, a trader, or even probably as a pilgrim. Unfortunately, the chronological as well as geographical distribution of such runic stones are uneven even in Scandinavia (Central Sweden has abundant amount of them, and most of them were erected around the beginning of the 2nd millennium, so rather late for the Viking Age, i.e. about the contemporary of the 'second Viking Age', characterized by the large-scale invasion of Danish fleet in England), so we cannot entirely rely on them to reconstruct the overall picture of the Vikings.
Another of few kind of this 'contemporary' source from Viking Age Scandinavia is Old Norse skaldic poems, only extant as the citations for contemporary testimonies of the events in later sagas, but while the verses offers vivid picture of the battles, they are often very difficult to interpret (even the 13th century Icelanders could make some mistakes), and generally say little to nothing on any statistic figures of the battle or plundering except for some place names. I would also like to add the fact that we can neither rely on the skaldic poems for the 9th century expansion of the Norsemen since the extant verses were predominantly those concerning the Norwegian rulers since the late 9th century.
Is it satisfactory to answer OP's question?
References:
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