Since I'm not a lawyer, I can not give you legal advice but what I learned in business school was: If you are truly a sub of a sub and receiving a 1099 at the end of the year, you are technically already a sub-contractor. In todays world you need to be Incorporated or a Limited Liability Company if you are not already. I would NEVER have a business with me as the Sole Proprietor. In the later case, if you get sued, they can take all of your personal assets, including your house and car. If you are Incorporated or a Limited Liability Company, they can only take the assets of that entity.
Now if you are asking about starting up a business you will need 4 things: a good lawyer that practices in the business field, (the lawyer will help you correctly set up your entity and review your contracts), a CPA to set up your books and file your taxes, (a non CPA can do the day to day stuff like payroll, billing and payables), a good business insurance agent, (not a home and auto only agent but one who understands workers comp and business general liability and bonds), and a banker unless you are independently wealthy, (it is best to have a relationship with a banker before you need to borrow money).
Lastly but just as important is contacts. You need to know the prime contractors and they need to know your ability. So make sure the prime contractor knows you and know your work is second to none.
Hope this helps. Good Luck my friend.