We have selected an all-sky (absolute value of b greater than or equal to 25 deg) 12 micron flux-limited sample of 893 galaxies from the IRAS Faint Source Catalog, Version 2 (FSC-2). We have obtained accurate total fluxes in the IRAS wavebands by using the ADDSCAN procedure for all objects with FSC-2 12 micron fluxes greater than 0.15 Jy and increasing flux densities from 12 to 60 microns, and defined the sample by imposing a survey limit of 0.22 Jy on the total 12 micron flux. Its completeness is verified, by means of the classical log N - log S and V/V(sub max) tests, down to 0.30 Jy, below which we have measured the incompleteness down to the survey limit, using the log N - log S plot, for our statistical analysis. We have obtained redshifts (mostly from catalogs) for virtually all (98.4%) the galaxies in the sample. Using existing catalogs of active galaxies, we defined a subsample of 118 objects consisting of 53 Seyfert 1s and quasars, 63 Seyfert 2s, and two blazars (approximately 13% of the full sample), which is the largest unbiased sample of Seyfert galaxies ever assembled. Since the 12 micron flux has been shown to be about one-fifth of the bolometric flux for Seyfert galaxies and quasars, the subsample of Seyferts (including quasars and blazars) is complete not only to 0.30 Jy at 12 microns but also with respect to a bolometric flux limit of approximately 2.0 x 10(exp -10) ergs/s/sq cm. The average value of V/V(sub max) for the full sample, corrected for incompleteness at low fluxes, is 0.51 +/- 0.04, expected for a complete sample of uniformly distributed galaxies, while the value for the Seyfert galaxy subsample is 0.46 +/- 0.10. We have derived 12 microns and far-infrared luminosity functions for the AGNs, as well as for the entire sample. We extracted from our sample a complete subsample of 235 galaxies flux-limited (8.3 Jy) at 60 microns. The 60 micron luminosity function computed for this subsample is in satisfactory agreement with the ones derived from the bright galaxy sample (BGS) and the deep high-galactic latitude sample, both selected at 60 microns.