Context: (Ultra)Luminous Infrared Galaxies [(U)LIRGs] are much more numerous at cosmological distances than locally, and are likely the precursors of elliptical galaxies. Studies of the physical structure and kinematics of representative samples of these galaxies at low redshift are needed in order to understand the interrelated physical processes involved. Integral field spectroscopy (IFS) offers the possibility of performing such a detailed analysis. Aims: Our goal is to carry out IFS of 42 southern systems which are part of a representative sample of about 70 low redshift (z ≤ 0.26) (U)LIRGs, covering different morphologies from spirals to mergers over the entire infrared luminosity range (L_IR = 1011-1012.6~L&sun;). Methods: The present study is based on optical IFS obtained with the VIMOS instrument on the VLT. Results: The first results of the survey are presented here with the study of two galaxies representative of the two major morphological types observed in (U)LIRGs, interacting pairs and morphologically- regular, weakly-interacting spirals, respectively. We have found that IRAS F06076-2139 consists of two low-intermediate mass (0.15 and 0.4 m_*) galaxies with relative velocities of ~550 km s-1 and, therefore, it is unlikely that they will ever merge. The VIMOS IFS has also discovered the presence of a rapidly expanding and rotating ring of gas in the southern galaxy (Gs). This ring is interpreted as the result of a nearly central head-on passage of an intruder about 140 million years ago. The mass, location and relative velocity of the northern galaxy (Gn) rules out this galaxy as the intruder. IRASF 12115-4656 is a spiral for which we have found a mass of 1.2 m_*. The ionized gas shows all the kinematic characteristics of a massive, fast rotating disk. The neutral gas traced by the NaI doublet shows distinct features not completely compatible with pure rotation. The neutral and ionized gas components are spatially and kinematically decoupled. The analysis presented here illustrates the full potential of IFS in two important aspects: (i) the study of the kinematics and ionization structure of complex interacting/merging systems, and (ii) the study of the kinematics of the different gas phases, neutral (cool) and ionized (warm), traced by the NaD and Hα lines, respectively.