Galaxies selected at 170um by the ISO FIRBACK survey represent the brightest ~10% of the Cosmic Infrared Background. Examining their nature in detail is therefore crucial for constraining models of galaxy evolution. Here we combine Spitzer archival data with previous near-IR, far-IR, and sub-mm observations of a representative sample of 22 FIRBACK galaxies spanning three orders of magnitude in infrared luminosity. We fit a flexible, multi-component, empirical SED model of star-forming galaxies designed to model the entire ~1-1000um wavelength range. The fits are performed with a Markov Chain Monte Carlo (MCMC) approach, allowing for meaningful uncertainties to be derived. This approach also highlights degeneracies such as between Td and beta, which we discuss in detail. From these fits and standard relations we derive: L_IR, L_PAH, SFR, tau_V, M_star, M_dust, Td, and beta. We look at a variety of correlations between these and combinations thereof in order to examine the physical nature of these galaxies. Our conclusions are supplemented by morphological examination of the sources, and comparison with local samples. We find the bulk of our sample to be consistent with fairly standard size and mass disk galaxies with somewhat enhanced star-formation relative to local spirals, but likely not bona fide starbursts. A few higher-z LIGs and ULIGs are also present, but contrary to expectation, they are weak mid-IR emitters and overall are consistent with star-formation over an extended cold region rather than concentrated in the nuclear regions. We discuss the implications of this study for understanding populations detected at other wavelengths, such as the bright 850um SCUBA sources or the faint Spitzer 24um sources.
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