If you are on an H1B, you need to get a US person co-founder and have them 'sponsor' you. Be wary about the start up failing because as soon as the sponsor breaks their contract, you will be out of status [1]. This means you may have to leave the country immediately.
The E5 visa [2] is the best alternative. If you can secure funding of around $500,000, you get the right to live and work in the US almost as a US person. You can work for yourself, travel in and out of the country as you wish, etc.
[1] http://www.klaskolaw.com/articles.php?action=view&id=8
> Terminated H-1B employees should be aware that time is not on their side. If the employee has plans to have another H-1B petition filed on his or her behalf, or to change to another nonimmigrant status, those plans should be implemented as quickly as possible.