Abstract At EuPRAXIA@SPARC_LAB an X-ray FEL user facility is driven by a plasma accelerator in the particle-driven configuration where an ultra-relativistic beam, the driver, through a plasma generates a wake of charge density useful for accelerating a witness beam. The electron bunches are generated through the so-called comb technique in an RF injector that consists of a 1.6-cell S-band gun followed by four S-band TW accelerating structures. The main working point foresees a 30pC witness and a 200pC driver longitudinally compressed in the first accelerating structure operated in the velocity-bunching regime, which allows to accelerate and manipulate the beam to reach proper transverse and longitudinal parameters. The optimization of the witness emittance is performed with additional magnetic field around the gun and the velocity bunching S-band structures and by shaping the laser pulse at the cathode. The paper reports on beam dynamics studies performed also with the insertion of an X-band RF cavity after the gun that is proposed to shape the beam current distribution and stabilize it with respect to RF jitters.