Carmen,
How you set-up your business is a personal decision and completely up to you. You could set-up a Sole Proprietorship, a LLC, or a Corporation (S-Corp or C-Corp). But I would set-up a business.
I would not recommend using your SSN. (It is really not smart to give your SSN to anyone these days, and if you operate as an individual you will need to give your SSN on your W-9 to the companies you work for so they can send you a year-end 1099.)
If you are going to be Sole Proprietorship, then I would recommend going to the
IRS website and applying for an tax id number in your business name, and not use your SSN for your business tax id. (This process is very easy. Just make sure to apply for your business name first. --See below.)
Furthermore I would make sure you go to your local Corporation Commission or Secretary of State website and apply for a business name/Trade Name. (Using a business name is more professional, and safer. I would use a business name as opposed to your personal name.)
Hope this helps,
Julie