The oracle bone findings from Anyang are the primary source of information on the Shang dynasty. Because they were communications to deity, they cover a wide range of topics from harvesting crops to human sacrificial instructions and contain thousands of characters. [1]

Virtually every work on the Shang dynasty references the oracle bones. Of course, the additional archeological artifacts and sites are vital for information, like the mass tomb in Anyang I mentioned in the other question about sacrifice.

As far as using the Shiji and other Han-period works, I'll defer to Gideon Shelach, professor of East Asian studies and archeologist specializing in Neolithic and Bronze Age of north China:

"The problem common to all these primary sources is that they were written during the latter part of the Eastern Zhou (771-221 B.C.) and the Han (206 B.C.-A.D. 220) periods. Although these later sources may rely in part on older documents, knowledge of some aspects of the Shang period was lost during a thousand years of oral transmission ... Further, the historical texts reflect a view of non-Han people as inferior to the Han. This means that descriptions regarding non-Shang people are even less reliable than the other contents of these documents."

The oracle bones are a fantastic resource and look into a bronze-age culture. They're similar to cuneiform or hieroglyphs in the sheer number of existing pieces and information.

Thanks for exploring the question further; I hope that helps!

[1] Qiu, Xigui (2000). Chinese writing (Wenzixue gaiyao). Transl. by Gilbert L. Mattos and Jerry Norman. Berkeley: Society for the Study of Early China.

[2] Shelach, Gideon. (1996). The Qiang and the Question of Human Sacrifice in the Late Shang Period. Asian Perspectives. Vol. 35, No. 1.