opening a LLC is not hard . Y ou just go to the secretary of state of where you want to business and then you have to fill out an application which basically ask you about how many owners, the place of the business office and for how long the LLC will be operating .You have to pay a fee of $250 and choose a name . and you wil obatain a LLC certificate in less than half an hour. After registering LLC you have to call IRS and obtain EIN;(EMPLOYERS IDENTIFICATION NUMBER). They dont exactly ask you for your G.C or your status. Check with state tax office if you need to obtain tax permit but to my knowledge you might not as you are selling service and services are tax free to the best of my knowledge)
Being a LLC you are liable for filing 941 (payroll taxes), 940 (annual version of payroll taxes) and annual tax return at the end of the year.
Ok  i believe you can do business on H1 but not on F1. And i am very much pleased with your idea of telemarketing business. Sounds exciting.My suggestion for you dont do business on OPT wait till you get your H1.