It depends on the type of business. In most urban and suburban areas there are zoning restrictions. If your company is a software company or a similair type of service related business, you can pretty much establish it anywhere. My own company was a home based business for the first 8 months.
Your choice of entity really depends on a lot of factors. I had several investors in the business and issueing shares was much easier to structure with a C-corp (Inc.). Some people start with an LLC since it allows for taxation pass through so you only pay taxes once, instead of twice for a corp (one at the corp level, and the other at employee/ shareholder level). Though, LLC laws are not as well developed in all States as is the case with corporation law.
The visa requirements for the business are that the business is established, registered and allowed to do business in the area where it is located.
It sounds like you need some help. I suggest you try to get in touch with a CPA and consult them about the options. You can do the same through a law firm but they are often a lot more expensive.