Documents to carry while traveling to USA

Currently I am in India, I never travelled to USA till now.
I got H1B pitetion approved from employer A in 2014 and also got the H1B stamping on my passport with employer A name on it and has validity upto June 2017.
But till now I didn’t get any onsite opportunities from employer A, so I approached a consultancy in USA and they are filed cap exempt pitetion for me.
This new cap exempt pitetion from employer B is also approved but I didn’t go for stamping again because employer B said that the existing stamping is sufficient to travel.

Below are my concern’s:

  1. Is my existing stamping is OK to travel to USA?
  2. Do I need to go for stamping process again for employer B?
  3. Can you please tell me the list of documents to carry while traveling to USA considering both employer A & B
  4. Few of my friends told me that Chicago is not the best place to choose it as port of entry, I have to go to OHIO can you please tell me the best place to choose as my port of entry other than Chicago?
  5. What would be the possible questions at Port of entry when having two pitetions from employers A&B and now travelling for employer B
  1. Yes

  2. No

  3. B’s petition and work documents. Employer contact details

  4. Is there no international airport in Ohio?

  5. They can ask why you changed employer, how you found B etc.