Taiwan: A New History edited by Murray Rubinstein is the standard academic survey — thorough, dense, and essential reading if you want a serious grounding in the island's past, from the Aboriginal era through Dutch colonialism, the Qing, Japanese occupation, and the Republic of China period.
The Generalissimo: Chiang Kai-shek and the Struggle for Modern China by Jay Taylor is the most balanced biography of the man whose regime dominated Taiwan for decades. Required context for understanding the Chiang Kai-shek Memorial Hall and much else.
Wild Fire: Sparks of Taiwan's Social Movement edited by Hanchao Lu — a collection of essays from the 1980s democracy movement. The passion still comes through in translation.
The Stolen Bicycle by Wu Ming-Yi is a novel that ranges across Taiwan's history through objects, memory, and the island's butterfly and insect life. Wu is Taiwan's most celebrated contemporary literary novelist and this is a good starting point. His earlier The Man with the Compound Eyes uses a piece of oceanic garbage to explore Taiwan's relationship with the sea.
Formosa Betrayed by George Kerr (1965) is a first-hand account by a US diplomat who witnessed the 1947 February 28 Massacre. Uncomfortable and essential — it explains a wound in Taiwan's history that still hasn't fully healed.
For practical travel reading, the Lonely Planet Taiwan guide is reliable for infrastructure and logistics. Supplement it with the Round Taiwan Round blog (rtaiwanr.com) for current, on-the-ground detail.