Husband getting Z type. Kids and I plan to join him in several months. What type visas do we need?

Tracey, you can apply for an S type to join him for several months.
If you can find a job after entering PRC with an S type, you can try to convert the S type to a work Z type in PRC after being employed. It is possible to be done while in PRC. If it cannot be done, you may need to exit and apply in your home country.