43 pages, 13 figures, accepted for publication in Astrophysical Journal Supplement Series ; This work presents the main ultraviolet (UV) and far-infrared (FIR) properties of two samples of nearby galaxies selected from the GALEX ($λ = 2315$Å, hereafter NUV) and IRAS ($λ = 60μ$m) surveys respectively. They are built in order to get detection at both wavelengths for most of the galaxies. Star formation rate (SFR) estimators based on the UV and FIR emissions are compared. Systematic differences are found between the SFR estimators for individual galaxies based on the NUV fluxes corrected for dust attenuation and on the total IR luminosity. A combined estimator based on NUV and IR luminosities seems to be the best proxy over the whole range of values of SFR. Although both samples present similar average values of the birthrate parameter b, their star-formation-related properties are substantially different: NUV-selected galaxies tend to show larger values of $b$ for lower masses, SFRs and dust attenuations, supporting previous scenarios for the star formation history (SFH). Conversely, about 20% of the FIR-selected galaxies show high values of $b$, SFR and NUV attenuation. These galaxies, most of them being LIRGs and ULIRGs, break down the downsizing picture for the SFH, however their relative contribution per unit volume is small in the local Universe. Finally, the cosmic SFR density of the local Universe is estimated in a consistent way from the NUV and IR luminosities.