The Empire podcast by William Dalrymple and Anita Anand has been fascinating and the first few episodes are exactly about the British East India Company.
I second this recommendation. A real eye-opener for me was learning that France and England were at it on India's east coast (the Carnatic wars) at pretty much the same time they were messing about the Hudson drainage basin in North America.
And that India was fabulously, spectacularly wealthy… like all of the gold and silver (taken and squandered in China by the Spanish) from the Americas plus some to spare.
"The Anarchy" and Kennedy's "The Rise and Fall of the Great Powers" make for great reading for the armchair historian.
I also loved the link between the behaviour of the British in India and the turn of sentiment in the Americas. What got me was the link between the tea in the tea-party and the famine inflicted in Bengal.
