Emission from protostars at centimeter radio wavelengths has been shown to trace the free-free emission arising from ionizing shocks as a result of jets and outflows driven by protostars. Therefore, measuring properties of protostars at radio frequencies can provide valuable insights into the nature of their outflows and jets. We present a C-band (4.1 and 6.4 cm) survey of all known protostars (Class 0 and Class I) in Perseus as part of the VLA Nascent Disk and Multiplicity (VANDAM) Survey. We examine the known correlations between radio flux density and protostellar parameters, such as bolometric luminosity and outflow force, for our sample. We also investigate the relationship between radio flux density and far-infrared line luminosities from Herschel. We show that free-free emission most likely originates from J-type shocks; however, the large scatter indicates that those two types of emission probe different time and spatial scales. Using C-band fluxes, we removed an estimation of free-free contamination from the corresponding Ka-band (9 mm) flux densities that primarily probe dust emission from embedded disks. We find that the compact (<1") dust emission is lower for Class I sources (median dust mass 96 M-circle plus) relative to Class 0 (248 M-circle plus), but several times higher than in Class II (5-15 M-circle plus). If this compact dust emission is tracing primarily the embedded disk, as is likely for many sources, this result provides evidence of decreasing disk masses with protostellar evolution, with sufficient mass for forming giant planet cores primarily at early times.