Seven hexagonal 2D materials consisting of elements of the IIIA and VA groups (BN, BP, BAs, AlN, GaN, GaP, and GaAs) were theoretically studied using first-principles methods. Simultaneous convergence in all principal parameters of the accurate many-body perturbational GW approach and the subsequent Bethe-Salpeter equation (BSE) was necessary to achieve precise fundamental and optical gaps, exciton binding energies, and absorbance spectra. Various convergence rates of studied properties in the case of different materials were visualized and explained. Benchmark calculations show several 2D materials from this set that strongly absorb in the visible and ultraviolet parts of the spectra, and therefore can be promising materials for (opto)electronic applications.