It's so funny that you should post this thread. The other day I had to do busy work for my job, so I had a cool linguistic history YouTube video playing in the background using auto-play. And basically, it got into the most widely spoken languages in the world. People love to focus on the European languages, but India OWNS in terms of sheer volume of people and the language spoken. I think India is important anyway in terms of language history - most European language, one way or another, descend from Sanskrit. So languages owe India a lot.
But anyway, to help you out, maybe you should go in order of most widely spoken languages in India. English is a good start of course, but here are the others on the list:
Bengali
Punjabi
Telugu
Marathi
Tamil
Urdu
Of course, these languages can also be quite regional, so think about what region of India you are going to be in and pick one on the list that is the most commonly spoken there. Also, if you get really proficient in the language, I think it will be an outstanding addition to your resume or LinkedIn. How many Westerners can say they know how to speak one of these? Good luck!