Since you have benefits through your work, then the first place you should check is your human resource office about the price of cobra coverage. It is law that if your employer has more than 20 employees then they have to send you a letter (I believe within 14 days) after you terminate your employment allowing you and all your dependents the opportunity to continue your/their healthcare coverage at your expense. You have to opt to take it within 60 days or you lose out. This is the best option if there is pre-existing conditions in your family (asthma, heart disease, any long-term maintenance medication conditions, etc.) for private insurance companies will make you fill out a questionaire and they are good at denying any claims they suspect are pre-existing. Cobra is good for 18 months and after that time you can usually convert it into a regular policy.
Here is the internet link to the government site explaining it in detail:
http://www.dol.gov/ebsa/faqs/faq_consumer_cobra.html
Also if you have children, check with your state about any children healthcare plans they may sponsor. Many states have raised the income qualification levels so many people who don't think they qualify actually do.