It also depends what state you are in. Many states crack down now on companies that 1099 software developers if the core business of the company is software. I would not want to deal with that mess, especially when DOL starts questioning you, because they want back-taxes from your "employer".
That said, highly recommend LLCing. Insurance companies seem to like that better, at least from my experience.
What insurance policies you will need? Well... if they are contracting your company, they probably will ask for proof of workers comp, general liability insurance, and some will even ask for errors and omissions. So get your rates way up, because you will need to make your money back on those expenses.