Dear Sir or Madam:
I would agree, you should take Form I-20 and perhaps even a copy of your application for OPT and employment authorization and school transcripts in a separate envelope to be presented only upon request to be on the safe side. This way you will be able to show that you are still within the authorized period of your F-1 visa.
Your passport, unexpired F-1 visa, I-20 form endorsed by the DSO, copy of the I-765 application and receipt, official transcripts showing completion of your studies, graduation and major, a letter from the company you'll work for confirming your job title, duties, compensation and start date, proof of financial ability (bank account statement e.g.) and anything indicating that you plan to return to India after your F-1 duration of status and OPT is completed.
Scott D. Pollock