Paul Theroux's best selling railway odyssey The Great Railway Bazaar takes you up and down India by train (and across most of the rest of Asia) and turns the whole world into a railway carriage. Engrossing, like most such books, as much for insights into the author as into the people he meets. Slow Boats to China by Gavin Powell follows much the same path but this time by boat and has interesting accounts of a number of boat trips around India. Slowly Down the Ganges by Eric Newby is another boat trip tale, this one borders, at times, on sheer masochism!
Karma Kola by Gita Mehta is accurately subtitled 'the marketing of the mystic east'. It amusingly and cynically describes the unavoidable and hilarious collision between India looking to the west for technology and modern methods while the west was descending upon India in search of ancient wisdom.
Ved Mehta has written a number of interesting personal views of India. Walking the Indian Streets (Penguin paperback) is a slim and highly readable account of the culture shock he went through on returning to India after a long period abroad. Portrait of India is by the same author. Ronald Segal's The Crisis of India (Penguin, London, 1965) is written by a South African Indian on the theme that spirituality is not always more important than a full stomach — a counter argument to all the praise of Hinduism and its spirituality. Readers have recommended Eating the Indian Air by John Morris; The Gorgeous East by Rupert Croft-Cooke; Delhi is Far Away and The Grand Trunk Road by John Wiles and books by Jan and Rumer Godden.
Finally no survey of personal insights into India can ignore V S Naipaul's two controversial books An Area of Darkness and India - A Wounded Civilisation. Born in Trinidad but of Indian descent Naipaul tells in the First book of how India, unseen and unvisited, had haunted him and the impact upon him when he finally did make the pilgrimage to the motherland. You may well find that much of this book rings very true with your own experiences while in India. In the second book he writes of India’s unsuccessful search for a new purpose and meaning for its civilisation.
If you want a thorough introduction to Indian history then look for the Pelican two volume A History of India. In volume 1 Romila Thapar follows Indian history from about 1000 BC to the coming of the Moghuls in the 16th century AD. Volume 2 by Percival Spear follows the rise and fall of the Moghuls through to India since independence. At times both volumes are a little dry but if you want a reasonably detailed history in a handy paperback format they’re worth having.
The Wonder that was India by A L Basham gives detailed descriptions of the Indian civilisations, origins of the caste system and social customs, detailed information on Hinduism, Buddhism and other religions in India and is very informative about art and architecture. It has a wealth of background material on ancient India without being overly academic.