An approach for the systematic determination of particularly stable hydride compositions C(n)H(2x) of a fullerene C(n) is presented. The study is divided into three parts. First, a CCSD(T) benchmark study on benzene and naphthalene hydrogenation is carried out. We show that the TPSS and BP86 functionals give more reliable relative isomer energies and reaction energies than B3LYP, when compared to CCSD(T) calculations. We therefore recommend BP86 for use on fullerenes. In the second part, a scheme for reduction in the immense number of possible fullerene hydride isomers is proposed. The scheme is based on thermodynamic sampling and involves density functional based tight binding as fast preselection method. The testing of the approach for C(60) constitutes the last part of the study. A low energy pathway for C(60)H(36) production is determined. Particularly stable structures are identified through analysis of the reaction energies along this pathway. These are C(60)H(2x) with 2x=18, 30, and 36. The good agreement of these results with the experimental and previous theoretical data suggests that our method is reliable and can be used to study fullerene hydrogenation.