Our family discovered Indian films in a big way after an Indian acquaintance suggested Baahubali (which we know is not, technically speaking, Bollywood). We'd seen Lagaan years before, loved it, but never knew where to go from there.
We instantly began exploring this fascinating new world. And love it!
This list is in no particular order.
For a good beginner's guide, try An American's Guide to Bollywood podcast.
They are two Americans who love Indian movies and want to help others do the same. Each episode they review an Indian movie from an American perspective, tell you how accessible it is to a westerner, where you can watch it, and if you might like it.