Theoretical models of galaxy formation suggest that the presence of an active galactic nucleus (AGN) is required to regulate the growth of its host galaxy through feedback mechanisms, produced by, for example, AGN-driven outflows. Although many observational studies have revealed that such outflows are common both at low and high redshift, a comprehensive picture is still missing. In particular, the peak epoch of galaxy assembly (1 < z < 3) has been poorly explored so far, and current observations in this redshift range are mostly limited to targets with high chances to be in an outflowing phase. This paper introduces SUPER (a SINFONI Survey for Unveiling the Physics and Effect of Radiative feedback), an ongoing ESO's VLT/SINFONI Large Programme SUPER will perform the first systematic investigation of ionized outflows in a sizeable and blindly-selected sample of 39 X-ray AGN at z similar to 2, which reaches high spatial resolutions (similar to 2 kpc) thanks to the adaptive optics-assisted IFS observations. The outflow morphology and star formation in the host galaxy will be mapped through the broad component of [O III]lambda 5007 and the narrow component of H alpha emission lines. The main aim of our survey is to infer the impact of outflows on the on-going star formation and to link the outflow properties to a number of AGN and host galaxy properties. We describe here the survey characteristics and goals, as well as the selection of the target sample. Moreover, we present a full characterization of its multi-wavelength properties: we measure, via spectral energy distribution fitting of UV-to-FIR photometry, stellar masses (4 x 10(9)-2 x 10(11) M-circle dot), star formation rates (25-680 M(circle dot)yr(-1)) and AGN bolometric luminosities (2 x 10(44)-8 x 10(47) erg s(-1)), along with obscuring column densities (up to 2 x 10(24) cm(-2)) and luminosities in the hard 2-10 keV band (2 x 10(43)-6 x 10(45) erg s(-1)) derived through X-ray spectral analysis. Finally, we classify our AGN as jetted or non-jetted according to their radio and FIR emission.