This is the first of two papers in which a study is made of a sample of 12 southern radio-luminous Seyfert galaxies. Our aim is to investigate possible correlations between radio morphology and nuclear/circumnuclear emission-line properties. In this paper we present radio images at 13, 6, and 3 cm taken with the Australia Telescope Compact Array (ATCA), global far-infrared (FIR) properties for the whole sample, and optical and near-infrared (NIR) spectroscopy of an interesting subset. We find a mixture of radio morphologies, including linear, diffuse and compact sources. When the FIR colors of the galaxies are considered there is an indication that the compact radio sources have warmer FIR colors than the diffuse sources, whereas the linear sources span a wide range of FIR colors. There is a wide variation in radio spectral-indices, suggesting that free-free absorption is significant in some systems, particularly IRAS 11249-2859, NGC 4507, and NGC 7213. Detailed emission-line studies are presented of 4 galaxies IC 3639, NGC 5135, NGC 3393 & IRAS 11249-2859. In IC 3639 we present evidence of vigorous, compact star formation enclosed by very extended [OI]6300 emission, suggestive of the boundary between a diffuse outflow and the surrounding ISM. In another galaxy, IC 5063, we see evidence for the possible interaction of a highly collimated outflow and the surrounding rotating inner disk. Of the 5 galaxies which show compact radio emission, 4 have radio/FIR flux ratios consistent with an energetically dominant AGN, whereas IC 4995 exhibits evidence for a very compact starburst.