Similar questions have been discussed over and over again. S corp is no because it cannot include non-resident alien shareholders.
LLC and C corps are fine. You can own a company in the US but as an H1B visa holder you CANNOT work for the company, which does not sponsor your visa, regardless you get paid or not. In another word you can only be a passive investor but can not manage day to day operation of the company.
If your relative will be operating the business, then it must register in that state as well. You will still need an in state registered agent. The company is formed in your state. The operation is in your state. The manager of the company is out of state. It just sounds too fishy.
