How is the host range of a virus determined?

The proteins on its surface and that on the surface is correct.

The protein in the host cytoplasm, whether its nucleic acid is DNA or RNA; the the enzymes carried by the virus and the enzymes produced by the virus before it infects the cell do not determine the host range of the virus.

Host range is important in viral attachment, attachment of a virus is a specific binding between viral capsid (surface) proteins and specific receptors on the surface of the host. This specificity determines the host range of a virus.