New Hire Through Contractor Company, Info for Family

You can, there are visit visas available but health insurance appears to be very difficult if not non existent and children cannot be enrolled in school.

Yes you can definitely bring your family but there are few things which you might have already considered but if not, need to consider or ask your sponsor.
1. To invite family we were required to get an NOC from our employer check with your employer if they will issue.
2. We have to pay for iqama for our family members and you will have to do the same which should be 400 Sar per person per month.
3. You can get a medical insurance for your family members.
4. Since you are hired on a single status on contract, check with your sponsor if they have any expectation for you to move around as people on contract are sometime have to shift depending on the job requirements. For school going kids it would be an issue.
5. Double check your work location and I hope it won't own be in the remote.
6. Check with your sponsor if they will be giving you rental allowance or a place to stay. That will have an impact on overall finance as they won't pay if bachelor housing is offered.