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 infrared (IR)-colour diagnostics. Using the weights assigned to the SFRS galaxies based on its parent sample, a far-IR-selected sample comprises 71 per cent H-II galaxies, 13 per cent Seyferts, 3 per cent transition objects (TOs), and 13 per cent low-ionization nuclear emissionline regions (LINERs). For the SFRS HII 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 HII 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-circle dot), median L(60 mu m) = 10(9) L-circle dot, median dust temperatures of F60/F100 = 0.36, and median L-H alpha surface density of 10(40.2) erg s(-1)kpc(-2), indicating older stellar populations as their main ionizing source rather than active galactic nucleus activity.