Context : Ultraluminous infrared galaxies are among the brightest objects in the local Universe . They are powered by strong star formation and/or an AGN . They are also likely to be the progenitors of elliptical galaxies . The study of the structure and kinematics of samples of local ULIRGs is necessary to understand the physical processes that these galaxies undergo , and their implications for our understanding of similar types of galaxies at high redshift . Aims : The goal of the project is to analyze the structure , dust distribution , ionization state , and kinematics of a representative sample of 22 ULIRGs . The galaxies in the sample undergo different merger phases ( they are evenly divided between pre- and post-coalescence systems ) and ionization stages ( 27 % H ii , 32 % LINER , 18 % Seyfert , and 23 % mixed classifications ) over a wide infrared luminosity range ( 11.8 \leq L _ { IR } /L _ { \odot } \leq 12.6 ) , with some galaxies of low-luminosity . The main aims of this paper are to present the sample and discuss the structure of the stellar and ionized gas components . Methods : Our study relies on the use of integral field optical spectroscopy data obtained with the INTEGRAL instrument at the William Herschel Telescope . Results : The structure of the ionized gas as traced by different emission lines has been studied and compared with that of the stellar continuum . We find structural variations between the gaseous and the stellar components , with offsets in the emission peaks positions of up to about 8 kpc . Young star formation ( as traced by the H \alpha emission ) is present in all regions of the galaxies . However , for 64 % of ULIRGs in an early interaction phase , the young star formation peak does not coincide with the stellar maxima . In contrast , galaxies undergoing advanced mergers have a H \alpha peak that is located in their nuclear regions . In three of the studied ULIRGs , hard ionizing photons traced by the [ O iii ] \lambda 5007 line excite extra-nuclear nebulae out to distances of about 7 kpc . These regions do not show bright stellar emission , but are rather dominated by nebular emission . These galaxies have nuclei classified as Seyfert in the literature . Approximately 40 % of the pre-coalescence ULIRGs exhibit shifts between the peaks of their red continuum and that local to the [ O i ] \lambda 6300 line . However , some of these peaks are associated with the secondary stellar nucleus of the system . In contrast , the emission in post-coalescence ULIRGs is concentrated towards the nuclei . These results imply that evolution caused by a merger is ocurring in the ionized gas structure of ULIRGs . Conclusions :