The zCOSMOS-SINFONI project is aimed at studying the physical and kinematical properties of a sample of massive z ~ 1.4-2.5 star-forming galaxies, through SINFONI near-infrared integral field spectroscopy (IFS), combined with the multiwavelength information from the zCOSMOS (COSMOS) survey. The project is based on one hour of natural-seeing observations per target, and adaptive optics (AO) follow-up for a major part of the sample, which includes 30 galaxies selected from the zCOSMOS/VIMOS spectroscopic survey. This first paper presents the sample selection, and the global physical characterization of the target galaxies from multicolor photometry, i.e., star formation rate (SFR), stellar mass, age, etc. The Hα integrated properties, such as, flux, velocity dispersion, and size, are derived from the natural-seeing observations, while the follow-up AO observations will be presented in the next paper of this series. Our sample appears to be well representative of star-forming galaxies at z ~ 2, covering a wide range in mass and SFR. The Hα integrated properties of the 25 Hα detected galaxies are similar to those of other IFS samples at the same redshifts. Good agreement is found among the SFRs derived from Hα luminosity and other diagnostic methods, provided the extinction affecting the Hα luminosity is about twice that affecting the continuum. A preliminary kinematic analysis, based on the maximum observed velocity difference across the source and on the integrated velocity dispersion, indicates that the sample splits nearly 50-50 into rotation-dominated and velocity-dispersion-dominated galaxies, in good agreement with previous surveys.