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We present a comprehensive catalog of observations and stellar population properties for 23 highly secure host galaxies of fast radio bursts (FRBs). Our sample comprises 6 repeating FRBs and 17 apparent nonrepeaters. We present 82 new photometric and 8 new spectroscopic observations of these hosts. Using stellar population synthesis modeling and employing nonparametric star formation histories (SFHs), we find that FRB hosts have a median stellar mass of ≈10^9.9M_⊙, mass-weighted age ≈5.1 Gyr, and ongoing star formation rate ≈1.3M_⊙yr⁻¹but span wide ranges in all properties. Classifying the hosts by degree of star formation, we find that 87% (20 of 23 hosts) are star-forming, two are transitioning, and one is quiescent. The majority trace the star-forming main sequence of galaxies, but at least three FRBs in our sample originate in less-active environments (two nonrepeaters and one repeater). Across all modeled properties, we find no statistically significant distinction between the hosts of repeaters and nonrepeaters. However, the hosts of repeating FRBs generally extend to lower stellar masses, and the hosts of nonrepeaters arise in more optically luminous galaxies. While four of the galaxies with the clearest and most prolonged rises in their SFHs all host repeating FRBs, demonstrating heightened star formation activity in the last ≲100 Myr, one nonrepeating host shows this SFH as well. Our results support progenitor models with short delay channels (i.e., magnetars formed via core-collapse supernova) for most FRBs, but the presence of some FRBs in less-active environments suggests a fraction form through more delayed channels.