Radio continuum emission at cm wavelengths is relatively little affected by extinction. When combined with far-infrared (FIR) surveys this provides for a convenient and unbiased method to select (radio-loud) AGN and starbursts deeply embedded in gas and dust-rich galaxies. Such radio-selected FIR samples are useful for detailed investigations of the complex relationships between (radio) galaxy and starburst activity, and to determine whether ULIRGs are powered by hidden quasars (monsters) or young stars (babies). We present the results of a large program to obtain identifications and spectra of radio-sleected, optically faint IRAS/FSC objects using the FIRST/VLA 20 cm survey (Becker, White and Helfand 1995). These objects are all radio-'quiet' in the sense that their radio power/FIR luminosities follow the well-known radio/FIR relationship for star forming galaxies. We compare these results to a previous study by our group of a sample of radio-'loud' IRAS/FSC ULIRGs selected from the Texas 365 MHz survey (Douglas et al. 1996). Many of these objects also show evidence for dominant, A-type stellar populations, as well as high ionization lines usually associated with AGN. These radio-loud ULIRGs have properties intermediate between those of starbursts and quasars, suggesting a possibile evolutionary connection. Deep Keck spectroscopic observations of three ULIRGs from these samples are presented, including high signal-to-noise spectropolarimetry. The polarimetry observations failed to show evidence of a hidden quasar in polarized (scattered) light in the two systems in which the stellar light was dominated by A-type stars. Although observations of a larger sample would be needed to allow a general conclusion, our current data suggest that a large fraction of ULIRGs may be powered by luminous starbursts, not by hidden, luminous AGN (quasars). While we used radio-selected FIR sources to search for evidence of a causal AGN/starburst connection, we conclude our presentation with a dramatic example of an AGN/starburst object from an entirely unrelated quasar survey selected at the opposite, blue end of the spectrum