Though it has a depressingly paltry pre-colonial section, I do suggest you check out the African section of our book list.

First of all, let me echo what /u/artrw has done in pointing you towards the reading list. It may not be huge, and it may not be comprehensive, but all of the texts there are not only well regarded as good, solid texts on their respective topics but they also comprise the foundation reads for most introductory courses on African history. You really cannot go wrong with most of them. Iliffe's Africans and Richard Reid's Warfare in African History are both fairly good introductory texts, although, obviously and by necessity, they lack the detail that other more focused regional texts can provide. As a basis for further reading though, they are both very good.

That being said, there are a few more texts which I would suggest to somebody like yourself who is looking for 'must-read' books.

Ralph Austen's African Economic History provides a clear understanding of the progression seen within the socio-economics of various African regions and peoples throughout the last few centuries, beginning in the pre-colonial period. His sections on the West African savannah empires and their economic ties with the Muslim north is particularly very good.

Similarly, Elizabeth Isichei's A History of African Societies to 1870 utilises some of the same socio-economic features identified in Austen and Iliffe's works to show how various African societies looked and acted and developed.

Finally, I also think that you should read Robert Collins' Problems in African History Vol.I (The Pre-Col Centuries). The point of this edited collection is to highlight the flaws and inherent difficulties faced by historians in attempting to discern social, economic, political and military histories about pre-colonial Africa. Although it is probably best to leave this until you perhaps understand some of the history which it talks about, it provides a very useful revision of what were some very dangerous assumptions regarding pre-colonial African history.

To give you a simple top 5 must reads (and the ideal order to read them) I would say:

i) Iliffe's Africans

ii) Austen's African Economic History

iii) Isichei's A History of African Societies

iv) Reid's Warfare in African History

v) Collins' Problems in African History

Obviously, if you realise you want to read more on, say, the military history of Africa then obviously shift towards that, or if you want to read on the later colonial interactions, there are books out there (and on the reading list) which will help you with that.