I suppose we don't have to discuss the following basic two-tier division among the (contemporary) sources in detail.

1. Written evidence
2. Non-written evidence, such as archaeological as well as osteological, and further, gene evidence mainly found in the mass grave during the 14th century.

1: Written Evidence

While several authors had already noticed the global scale of the ongoing outbreak of the Black Death in the middle of the outbreak itself (just before ca. 1350 CE), such as the mention of Chinese/ 'Indian' origin of the plague, no single contemporary text could cover the entire extent of the outbreak across Eurasia. Thus, our timeline/ map of the spread of the Black Death (linked to the map in History Today, largely based on Benedictow's monograph) is primarily modern reconstruction of the event, based on the patchwork of the contemporary (and some are even later) texts, as is often the case as such a global and significant event in history.

It also means that we cannot generally rely on the written account on the Black Death for its spread into the area that lacked the reliable contemporary account, such as sub-Saharan Africa.

The first and foremost problem of such a situation in the primary source is the difficulty of accessing and reading the relevant sources, consisting of diverse language, nature (thus also, different trustworthiness of their descriptions). Fortunately, we have two convenient primary source collections, summarized by Horrox and Aberth respectively, with an useful introduction, consisting not only of Latin, but also of various vernacular languages, and even some Byzantine and Islamic text (Horrox ed. 1994; Aberth ed. 2017).

(Added:) The followings are some examples of the contemporary or near-contemporary key texts that narrated the early spread of the plague, mainly following the track of contemporary Mediterranean trade:

• Essay on the Report of the Pestilence (ca. 1348) by Abu Hafs Umar Ibn Al-Wardi (Aberth ed. 2017: 23-25).
• The History of the Disease (historia de morbo) (ca. 1356) by Gabrielle de Mussis (Horrox ed. 1994: 14-26; Aberth ed. 2017: 135f., though Aberth's 1st ed. features the excerpt of de Mussis more extensively).
• Chronicle (ca. 1361) by Michele da Piazza, Sicilian Monk (Horrox ed. 1994: 35-41; Aberth. ed. 2017: 80-84).

It is true, however, even now researchers have continued their critical re-reading of these texts to improve their reconstruction of the geographical as well as chronological spread of the outbreak, as Green argues against the classical account, based on de Mussis' the transmission of the plague during the Siege in Crimean Peninsula (Green 2020).

2: Non-Written Evidence

I summarized current scholars' use of non-written evidence, such as the archaeological excavation of the mass grave, gene analysis from the remains, and also land use in What effects of plagues and other huge epidemics can we see in archaeology?, so if you are interested in them, please also refer to the linked thread.

References:

• Aberth, John (ed.). The Black Death, The Great Mortality of 1348-1350: A Brief History with Documents. 2nd ed. New York: MacMillan, 2017.
• Horrox, Rosemary (ed.). The Black Death. Manchester: Manchester UP, 1994..

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• Benedictow, Ole J. The Black Death 1346-1353: The Complete History. Woodbridge: Boydell, 2004.
• ________. 'The Black Death: The Greatest Catastrophe Ever'. History Today 55-3 (2005)
• Monica H. Green, 'The Four Black Deaths', The American Historical Review, Volume 125, Issue 5, December 2020, Pages 1601–1631, https://doi.org/10.1093/ahr/rhaa511