For a basic intro for India, there are two books I'd really suggest anyone to read:
- Penguin History of Early India by Romila Thapar
- The Wonder That Was India - Volume 1 by Arthur Llewellyn Basham
Both cover the general Indian history very well, including the period from the Imperator Rome timeline.
Thanks for these, it's really hard to find a good, reliable and unbiased history of early India. I've added the first one, don't have access to the other online, but will check out the physical copy in the uni library and probably add it too.
The list also now has sections added on India and Central Asia, Warfare, Eastern Europe and Ancient Sources since I last gave an update. Some other titles have been added in here and there. Keep the suggestions coming!