Here are a few books that you might find useful:
Mindfulness in Plain English, Henepola Gunaratana. 1992. Wisdom Publications. Excellent practical introduction to mindful meditation.
What the Buddha Taught, Walpola Rahula. 1974. Grove Press. Well-respected collection of translations of Buddhist Sutras. Useful for reference with thoughtful notes.
Cutting Through Spiritual Materialism, Chogyam Trungpa, 1973. Shambhala – a very popular book, that many people find useful – by a charismatic Tibetan teacher.
The Way of Zen, Alan Watts. 1989. Vintage. First published in 1957, but still an excellent, very readable introduction to Zen, Daoism and Buddhism in general.
Zen Mind, Beginner’s Mind, Shunryu Suzuki. 1970. Weatherhill. Another good introduction with a lot of practical advice.
Moon in a Dewdrop: Writings of Zen Master Dogen, ed. Kazuaki Tanahashi. 1995. North Point Press.
The Art of Just Sitting: Essential Writings on the Zen Practice of Shikantaza, Ed. John Daido Loori. 2002. Wisdom Publications. Very good collection of helpful essays on Zen meditation.
Essential Writings, Thich Nhat Hanh. 2001. Orbis Books. A useful selection of writings by a very influential Buddhist teacher.
Confession of a Buddhist Atheist, Stephen Batchelor, 2010. Spiegel & Grau. A provocative but very thoughtful book by a contemporary Buddhist teacher grounded in Tibetan and Korean Zen traditions – but arguing for a new form of Buddhism to suit contemporary western contexts.
After Buddhism: Rethinking the Dharma for a Secular Age, Stephen Batchelor. 2015. Yale University Press. Thought-provoking book by an influential writer on ‘secular Buddhism’.
The New Buddhism, James William Coleman, 2001. Oxford University Press – an overview of the development of western Buddhism up to the 1990s.
And lastly, a couple of texts on mindfulness in a secular therapeutic context:
The Mindful Way through Depression, eds. Williams, Teasdale, Segal and Kabat-Zinn, 2007. Guilford Press – a very influential practical guide.
Wherever You Go, There You Are, Jon Kabat-Zinn, 2004. Piatkus Books – about mindfulness in everyday life.
Early Buddhist texts – links:
The Pali Canon – Source Texts for Secular Buddhism, compiled by Stephen Batchelor: http://www.stephenbatchelor.org/media/Stephen/PDF/Stephen_Batchelor-Pali_Canon-Website-02-2012.pdf
The Word of the Buddha – extracts from the Pali Canon – a very well respected, but early, translation by Nyanatiloka Mahathera – 1907, revised ed. 1967 – (also available as a small book – published by the Buddhist Publication Society: http://www.urbandharma.org/pdf/wordofbuddha.pdf
The Authenticity of the Early Buddhist Texts by Bhikkhu Sujato & Bhikkhu Brahmali, Oxford Centre for Buddhist Studies: http://ocbs.org/wp-content/uploads/2015/09/authenticity.pdf
A Theravada Library – more extracts from the Pali Canon by various respected translators: http://www.accesstoinsight.org/lib/