More can be said by a proper specialist (I'm not an Andeanist, sadly), but I'm sure I can get you started!
There are quite a few overviews of precolonial Andean history, and these will generally have an even-handed focus which will give you lots of detail on pre-Inkan societies. Which of these is best will depend on your preferences as regards detail and form, so I'll provide commentary on each.
- Adams, Richard E. W.. 1997. Ancient Civilizations of the New World. Abingdon: Routledge. If you're looking for a much more general treatment, Adams' book is solid. It's very short indeed, and the amount of focus on the pre-Inkan Andes specifically is not great - not much more than a sixth of the book, as opposed to Quilter's book, which in the previous edition was ~80% on pre-Inkan stuff - but then again it's cheap and gives you a nice overview of other areas of Americanist archaeology.
- Keatinge, Richard W. (ed.). 1988. Peruvian prehistory: An overview of pre-Inca and Inca society. Cambridge: Cambridge University Press. Keatinge's volume is more technical than the other two, and is a collection of essays rather than a single thesis by a single author. It's a bit patchier than the other two as a result, but also has more variety and depth than they do. Its focus on pre-Inkan matters is more of like Quilter's than Adams'.
- Quilter, Jeffrey. 2022. The Ancient Central Andes, 2nd edn.. Abingdon: Routledge. This is probably the best synthesis for a beginner, and has just got a lovely new edition. It covers everything from the first humans in the Andes to colonial society (which is pushing the "ancient" bit, really, but oh well). Quilter himself is a Moche specialist, so he's very strong on pre-Inkan periods, especially the Early Intermediate Period (during which the Moche flourished). It's a digestible length and scholarly without being inaccessible at all, but is of course all from the perspective of one scholar.
- Tantaleán, Henry. 2021. The Ancient Andean States: Political Landscapes in Pre-Hispanic Peru. Abingdon: Routledge. This one's also quite technical, but still works as an overview and can be read by confident beginners with some background in archaeology. As you may be able to tell from the title, it's more specific in focus than the other three, and is advancing a specific thesis rather than just trying to give a synthesis of the field. Nevertheless, I quite like it.
Alongside overviews, you can also find more specific books to dive into specific societies. My main interest is the Moche, so my grasp of the best books for other periods is shakier - be warned! My knowledge of the palaeoanthropological literature on Preceramic societies is outright bad, so I'm afraid you'll have to hope for someone else, or mine the bibliography of an overview. I'd recommend reading at least one overview before jumping into something like this, but, hey, you can do whatever you want.
- Bawden, Garth. 1997. The Moche. Oxford: Blackwell Publishers Ltd. A classic on the Moche, a deeply interesting society of the Early Intermediate Period, centuries before the Inka. Not too big and aimed at people unacquainted with Moche archaeology and history, and in general a good place to start with more specific studies.
- Benson, Elizabeth P.. 2012. The Worlds of the Moche on the North Coast of Peru. Austin: University of Texas Press. Benson very much wrote the book on the Moche in English (in 1972), and this book is a great up-to-date version. It has a stronger artistic and religious focus than some books, but still gives a strong overview of all topics.
- Burger, Richard L.. 1995. Chavin and the Origins of Andean Civilization. London: Thames & Hudson Ltd. A great overview of the Chavín culture of the Early Horizon, an immensely influential religious phenomenon (or polity? or culture? there's a lot of uncertainty). As you might suspect from the publisher name, illustrations are provided liberally.
- Janusek, John Wayne. 2008. Ancient Tiwanaku. Cambridge: Cambridge University Press. A pretty solid overview of Tiwanaku, a highly influential polity that came just after the Moche in the Middle Horizon. It also significantly predates the Inka. It's aimed at novices too, but is I think a little on the drier and more technical end.
- Kolkata, Alan L.. 1993. The Tiwanaku: Portrait of an Andean Civilization. Oxford: Blackwell Publishers Ltd. Quite a systematic treatment of Tiwanaku history, going from analytical perspectives to a more narrative element. I tend to like this sort of organization, but some people may like it less or find it harder going, starting with the analysis and only later getting the narrative. Nevertheless, it again assumes basically no background knowledge, and is an even-handed overview.
- Silverman, Helaine and Proulx, Donald A.. 2002. The Nasca. Oxford: Blackwell Publishers Ltd. Another nice synthesis aimed at novices to Nasca archaeology. A really balanced look at different elements of culture, society, and history, and a nice length.
I'm sorry this is so limited and patchy. Again, I hope someone more qualified than me can come along. Best of luck getting into Andean archaeology, though! It's a fascinating field.