We are traveling to India in March and April 2017.
You can register on irctc the web portal for booking train tickets in India, but the interface is very clunky.
I would personally advice you to reach out a local verified travel agent in India and ask them to do all the bookings for you. Agents charge anywhere between $3-$10 per ticket which will not affect your budget a lot but it will make life a lot easier. For other bookings like flights and cabs you can easily use one of the many online portals.