Density functional theory calculations of the electronic structure of graphane and stoichiometrically halogenated graphene derivatives (fluorographene and other analogous graphene halides) show: (i) localized orbital basis sets can be successfully and effectively used for such two-dimensional materials; (ii) several functionals predict that the band gap of graphane is greater than that of fluorographene, whereas HSE06 gives the opposite trend; (iii) HSE06 functional predicts quite good values of band gaps with respect to benchmark theoretical and experimental data; (iv) the zero band gap of graphene is opened by hydrogenation and halogenation and strongly depends on the chemical composition of mixed graphene halides; (v) the stability of graphene halides decreases sharply with increasing size of the halogen atom--fluorographene is stable, whereas graphene iodide spontaneously decomposes. In terms of band gap and stability, the C(2)FBr and C(2)HBr derivatives seem to be promising materials, e.g., for (opto)electronics applications, because their band gaps are similar to those of conventional semiconductors, and they are expected to be stable under ambient conditions. The results indicate that other fluorinated compounds (C(a)H(b)F(c) and C(a)F(b)Y(c), Y = Cl, Br, I) are stable insulators.