We report first principles modeling of partially hydrogenated graphene, with a variety of hydrogen induced superstructures. The dependence of the optical gap on hydrogen content and coverage is examined, to assess the best configurations suitable for optoelectronic applications. Electron and optical DFT LDA gaps in the range between 0.2 and 1.5 eV were obtained for low hydrogen coverage. For such systems, hydrogen clustering (by saturating neighbouring C dangling bonds at the opposite sides of the graphene sheet) is energetically most favourable and generally produces larger gap. More homogeneous H distribution one-side bonded to C-host atoms is, in contrast, less energetically favourable or even structurally unstable and generally produces smaller gap. In addition, ordering of hydrogen was observed at 50% of H, that offers a possibility of transforming 2D graphene to an array of 1D nanowires Calculated linear optical anisotropy and nonlinear second harmonic generation (this will be discussed in a forthcoming paper) indicate these are not only gap sensitive, but can provide an access to microscopic details of the 2D nano-sheets such as symmetry, hydrogen induced structure, degree of hydrogenation, chemical bonding and many others, all promising for device application. The approach developed can be used for graphene/ graphane single layer or bilayer, formed on top of various substrates, where experimental geometries may not provide conditions for complete hydrogenation of the 2D nano-sheet(s).