The answer is yes you can do this. In fact, my colleagues and I represent several Indian companies that have wholly owned subsidiaries here in the U.S. l.
I have been advised by my Indian clients that Indian nationals are prohibited by Indian law from owning property in the U.S. However, what you can do is to create a limited liability company (LLC) or a "C" corporation (S corporations are helpful in the U.S. for tax purposes, but foreign nationals may not hold stock in an S corporation). You would hold the membership interest in the LLC or the shares of the corporation.
You will need an EIN here as you will have to report income to the U.S. Whether you will pay taxes on profits in India or the U.S. is a question for tax counsel. I believe there is a treaty between our countries that will protect you in the main from double taxation.
As to where, the threshold question is whether you plan to have operations here or whether your services will be completely on line. I generally prefer Delaware as a state for organization when one has no strong ties to any other state. If you are thinking in terms of a physical facility, I would be inclined to suggest Northern Virginia among other areas. California is a center for tech activity, but dealing with the California government can be a challenge, in my view. And it is more costly.
As to insurance and taxes, again it depends on what the nature of your activities are. If you have a physical facility, then you need liability insurance. If you have employees, you need to be concerned with workers compensation and unemployment insurance. If you sell goods or in some states even if you sell services, you may need to collect sales tax.
Finally, as to visas, if you were to invest $500,000 to $1 million and if you were to create 10 jobs over a two year period, you could get an EB5 visa in all likelihood. That would pretty much assure you a green card to allow you to operate with relative ease. On the other hand, there are other visas that can be obtained for periodic trips to the U.S.
I would be happy to discuss the matter with you further. One of my partners is from India, and we represent several Indian companies with operations in the U.S. I have other Indian clients, though they have immigrated to the U.S.
With kindest regards,
Congrats on your interest in starting a U.S. based business. You don't need a visa or to be a citizen to start a business in the U.S. You would need a visa if you wanted to work in the business however.
All the questions you ask are reasonable questions to ask in your situation, however you need they would be more appropriately answered in a one on one conversation with the attorney where they can ask you questions.
There are several attorneys who may be willing to do so via email or skype.