won't cost an arm and a leg? I live in NYC and I recently resigned from my previous job to be an independent contractor and now my children and I have no health insurance. What are the best insurance plans out there for someone in NYC, with low monthly cost?

Probably one that offers a health savings plan. The premiums are lower but the deductibles are high. The point is that you should put money into this savings account that you can later apply to your out of pocket or deductible. This money belongs to you and is tax deductible.