Can anyone on either F1 or H1B visa status start a company like 'online marketing home business' and run it? If yes, then what kind of business structure is permitted and best suitable - Sole proprietor, general partnership, limited partnership, LLC (Limited Liability Company), S Corporation or C Corporation?

After some research on the web I found in some forum that F1/H1B visa holder can start/own companies but cannot work for it and receive income but instead hire a Green card holder or citizen to work for it in some executive position, is this correct? Some also suggest that sole proprietorship, S corporation are not possible for H1/F1 holders. Is LLC the best business structure for the company? Or, is there a possibility of opening a business in partnership with a GC/citizen?