This is a great question.  If you have group coverage now, you should be offered COBRA or State Continuation coverage.   As long as you were covered by an employer plan you can get individual health coverage under the SEP (Special Enrollment Period).  You will have 60-days from the loss of coverage under the group to make a transition to a individual insurance policy.  You can purchase these policies through HealthCare.gov if you are getting a subsidy or directly from a carrier if you are not eligible for a subsidy.  You can work with an agent or broker to help you compare and find the best plan for you needs.

If you make one COBRA or State Continuation payment, you will lose the SEP enrollment period for individual health plans.  I would find out the premiums for the COBRA and State Continuation to ensure that it is not less expensive than the individual market.  

One other caution is the enrollment deadline on enrolling you must enroll by 15th to have coverage on the first of the next month, if you enroll on the 16th, it will be pushed out to the first of the month after next.

I would suggest working with a local agent to ensure you are doing the best thing for your family.