This is the first of a series of papers aimed at characterizing the populations detected in the high-latitude sky of the Fermi-LAT survey. In this work, we focus on the intrinsic spectral and flux properties of the source sample. We show that when selection effects are properly taken into account, Fermi sources are on average steeper than previously found (e.g., in the bright source list) with an average photon index of 2.40 +/- 0.02 over the entire 0.1-100 GeV energy band. We confirm that flat spectrum radio quasars have steeper spectra than BL Lacertae objects with an average index of 2.48 +/- 0.02 versus 2.18 +/- 0.02. Using several methods, we build the deepest source count distribution at GeV energies, deriving that the intrinsic source (i.e., blazar) surface density at F-100 >= 10(-9) ph cm(2) s(-1) is 0.12(-0.02)(+0.03) deg(-2). The integration of the source count distribution yields that point sources contribute 16(+/- 1.8)% (+/- 7% systematic uncertainty) of the GeV isotropic diffuse background. At the fluxes currently reached by LAT, we can rule out the hypothesis that pointlike sources (i.e., blazars) produce a larger fraction of the diffuse emission.
