We present activity demographics and host-galaxy properties of infrared-selected galaxies in the local Universe, using the representative Star Formation Reference Survey (SFRS). Our classification scheme is based on a combination of optical emission-line diagrams (BPT) and IR-color diagnostics. Using the weights assigned to the SFRS galaxies based on its parent sample, a far-infrared-selected sample comprises 71% H,textsc{ii} galaxies, 13% Seyferts, 3% Transition Objects (TOs), and 13% Low-Ionization Nuclear Emission-Line Regions (LINERs). For the SFRS H,textsc{ii} galaxies we derive nuclear star-formation rates and gas-phase metallicities. We measure host-galaxy metallicities for all galaxies with available long-slit spectroscopy and abundance gradients for a subset of 12 face-on galaxies. The majority of H,textsc{ii} galaxies show a narrow range of metallicities, close to solar, and flat metallicity profiles. Based on their host-galaxy and nuclear properties, the dominant ionizing source in the far-infrared selected TOs is star-forming activity. LINERs are found mostly in massive hosts (median of $10^{10.5}$ M$_{odot} $), median $L(60mu m) = 10^{9}$ L$_{odot}$, median dust temperatures of $ F60/F100 = 0.36 $, and median $L_{textrm{H}alpha}$ surface density of $ 10^{40.2} $ erg s$ ^{-1} $kpc$ ^{-2} $, indicating older stellar populations as their main ionizing source rather than AGN activity.