Hi, Buddhist historian here. Here is a list to get you started:

• A Concise History of Buddhism by Andrew Skilton; Perhaps the simplest introduction to Buddhist history, but what it lacks in completeness, it makes up for in readability.
• The Buddhist Religion: A Historical Introduction By Richard Robinson, Willard L. Johnson, and Ṭhānissaro Bhikkhu; Slightly more comprehensive than Skilton's book, but much more like a text book. It is a good introduction nonetheless.
• Theravāda Buddhism: A Social History From Ancient Benares to Modern Colombo By Richard F. Gombrich A more focused work specifically on the Theravāda form of Buddhism practiced in Southeast Asia and Śrī Lankā. Gombrich's work is divisive for his textual approach but ultimately is highly regarded
• Indian Buddhism by A.K. Warder The standard history of Buddhism in India, it is somewhat dated at points, specifically in it's work on the decline of Buddhism, which Warder blames primarily on Turkish Muslim invasions, but good nonetheless.
• Mahāyāna Buddhism: The Doctrinal Foundations By Paul Williams; I personally go back and forth on Williams more personal style of writing and dislike some of his analysis, but this is a good intro to the development of Mahāyāna both in India and beyond. This hits all the key points of Mahāyāna's development.
• In the Buddha's Words: An Anthology of Discourses from the Pāli Canon by Bhikkhu Bodhi; A compilation of discourses from the Pāli canon and an introduction to Theravāda philosophy and the primary sources. Written in a readable and organized manner with commentary and footnotes to elucidate the meaning of certain terms.

More Specialized works inclued;

• Early Buddhist Theory of Knowledge by KN Jayatellike; Exactly what it says on the tin, probably the most influential work on Early Buddhism and pre-Dignāga Buddhist Logic and epistimology.
• The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophy by Thomas McEvilley ; an absolutely breathtaking work of comparative philosophy. I don't always agree with McEvilley's conclusions but his work is invaluable to any comparative study.
• Religions of the Silk Road: Premodern Patterns of Globalization by Richard Foltz ; Not focused exclusively on Buddhism, but on how religions spread along the Silk Road, which Buddhism did.
• The Making of Buddhist Modernism by David L McMahn; Focuses on the evolution of Buddhism in the last 150 years worldwide in order to accommodate modernity.
• Buddhism in China: A Historical Survey by Kenneth Ch'en; An in depth look at the history and evolution of Buddhism in China from the Han to Mao
• Studies in the Origins of Buddhism by Govind Chandra Pande; A dated but nonetheless comprehensive text examining the Pāli canon linguistically to date it. The methodology is sound, but some conclusions seem flawed. In any case, valuable.
• The Authenticity of the Early Buddhist Texts by Bhikkhu Sujato and Bhikkhu Brahmali; A somewhat flawed, but quite good work arguing for the authenticity of EBTs using linguistic analysis, comparative analysis, and textual analysis. Rather short and readable

There are more, but that should be enough to start you off for a few months at least. I would recommend starting with one of the introductions and either studying Mahāyāna or Theravāda next since they start to diverge around the 3rd century CE when Buddhism leaves India in a big way.

Not to discourage any recommendations (because the more the merrier) but

What if I told you there's an awesome reading list that's perpetually updated by the knowledgable flairs and mods?

A few subsections that might interest you include:

Cultural, Intellectual and Religious History (The subsection Religious history has some recommendations on China)

East Asia

Southeast Asia