Government Schools

I would like to enroll a boy into a government school,as it is free ,and have him additional educated by a private teacher.I wanted to enroll him in the nearest by school but after some closer looks this one will be too primitive.

Now I have seen many schools in the area which seem also to be government schools but which look more clean and regulated.

My question now is,are all government schools free or is there a difference and how to distinguish them.

Will he be allowed to enroll at any govrment school or only the one in the district he is registered?Thanks