There are an absolute ton of good sources, and that's just counting the ones in English! Hopefully this list won't be too many sources...

Primary sources:

Muslim sources:

Francesco Gabrieli, Arab Historians of the Crusades, trans. E. J. Costello (University of California Press, 1969) - Gabrieli has lots of snippets from various Islamic authors, including several dealing with Saladin

Baha ad-Din, The Rare and Excellent History of Saladin, trans. D.S. Richards (Ashgate, 2001) - Baha ad-Din was Saladin's secretary and was present for the Third Crusade and the later part of Saladin's life. He wrote this biography of Saladin, but it's almost more of a hagiography

The Chronicle of Ibn Al-Athir for the Crusading Period, trans. D.S. Richards (Ashgate, 2007) - this translation is 3 volumes, and volume 2 is about Saladin’s time period. Ibn al-Athir was a later 13th-century historian but he knew Saladin's family well

Christian accounts:

Peter W. Edbury, The Conquest of Jerusalem and the Third Crusade: Sources in Translation (Ashgate, 1996) - most of this is the so-called "Old French continuation of William of Tyre". William was the Latin historian of the Kingdom of Jerusalem in the 12th century but he died before the Third Crusade. His chronicle was translated into French and continued by other anonymous authors who were present for the crusade.

The Chronicle of the Third Crusade: The Itinerarium Peregrinorum et Gesta Regis Ricardi, trans. Helen J. Nicholson (Ashgate, 1997) - more sources from the Third Crusade, but from the perspective of European crusaders

Ambroise the Poet, History of the Holy War, trans. Marianne Ailes (Boydell, 2003) - Ambroise was another European crusader

Modern secondary sources:

Biographies of Saladin:

Stanley Lane-Poole, Saladin and the Fall of the Kingdom of Jerusalem (Putnam, 1906) - this is now very very old and very out of date, but it’s a good example of the older English scholarship that depicted Saladin as a noble and chivalrous knight

Andrew S. Ehrenkreuz, Saladin (SUNY Press, 1972)

M.C. Lyons and D.E.P. Jackson, Saladin: The Politics of the Holy War (Cambridge University Press, 1984)

Anne-Marie Eddé, Saladin (Flammarion, 2008, originally in French but translated into English in a 2014 edition by Jane Marie Todd)

Jonathan Phillips, The Life and Legend of the Sultan Saladin (Penguin, 2019)

General works covering Saladin's time period:

Diana Abouali, “Saladin's Legacy in the Middle East before the Nineteenth Century,” in Crusades 10 (2011)

Niall Christie, Muslims and Crusaders: Christianity’s Wars in the Middle East, 1095-1382, From the Islamic Sources (Routledge, 2014)

Paul M. Cobb, The Race for Paradise: an Islamic History of the Crusades (Oxford University Press, 2014)

John Gillingham, Richard I (Yale University Press, 1999)

Carole Hillenbrand, The Crusades: Islamic Perspectives (Routledge, 1999)

John D. Hosler, The Siege of Acre, 1189-1191 (Yale University Press, 2018)

Alex Mallett, Medieval Muslim Historians and the Franks in the Levant (Brill, 2014)

I hope that's not too overwhelming, I know it's a lot of stuff.

The best thing to do would probably be to start with Jonathan Phillips' book, since it's the most recent one and it has the most up-to-date research. It's very easy to read, not too heavy and full of notes like academic books can be.