Using the new version of the photoionization code Titan designed for plane-parallel photoionized thick hot media, which is unprecedented from the point of view of line transfer, we have undertaken a systematic study of the influence of different parameters on the He-like and H-like emission of a medium photoionized by an X-ray source. We explain why in modelling the emitting medium it is important to solve in a self-consistent way the thermal and ionization equilibria and to take into account the interconnection between the different ions. We insist on the influence of the column density on the He-like ion emission, via stratification of ion species, temperature gradient, resonance trapping and continuum absorption, and we show that misleading conclusions can be deduced if it is neglected. In particular a given column density of an He-like ion can lead to a large range of total column densities and ionization parameters. We show also that there is a non-model-dependent relation between an ion column density and its corresponding temperature, and that the ion column density cannot exceed a maximum value for a given ionization parameter. We give the equivalent widths of the sum of the He-like triplets and the triplet intensity ratios G and R, for the most important He-like ions, for a range of density, column density, and ionization parameter, in the case of constant density media. We show in particular that the line intensities from a given ion can be accounted for, either by small values of both the column density and of the ionization parameter, or by large values of both quantities, and it is necessary to take into account several ions to disentangle these possibilities. We show also that a ``pure recombination spectrum" almost never exists in a photoionized medium: either it is thin, and resonance lines are formed by radiative excitation, or it is thick, and free-bound absorption destroys the resonance photons as they undergo resonant diffusion. Consequently, the G ratio is much smaller than the pure recombination ratio for a small value of the total column density, and it exceeds the recombination ratio for large values of the total column density and of the ionization parameter.