Laser wakefield acceleration of GeV electrons is becoming a mature technique, so that a reliable accelerator delivering stable beams to users communities can now be considered. In such a context, two plasma stages, one injector and one booster stage, offer a flexible solution for optimization. For the injector we consider here the resonant multipulse ionization injection (ReMPI) that can be optimized to generate electron bunches with high enough quality to be efficiently transported to the second stage. In order to better control the beam-loading effect and optimize the beam manipulation after the plasma downramp, a quasiround beam is preferable. In this respect, we present analytical and particle-in-cell results concerning the tunnel-ionization process in presence of two, orthogonally polarized, laser pulses with different wavelengths. We also show, by means of hybrid fluid/PIC numerical simulations, that a stable working point with the ReMPI injector exists at 32 pC, 4 kA peak current, with mean energy of 150 MeV, energy spread of 1.65% rms, normalized emittance Ļµ n Ā¼ 0.23 Ī¼m and divergence of 0.6 mrad. The scheme relies on a 150 TW Ti:Sa laser modified to achieve a four-pulses driver train and a third harmonics ionization pulse.