We present the chemistry, temperature, and dynamical state of a sample of 193 dense cores or core candidates in the Perseus Molecular cloud and compare the properties of cores associated with young stars and clusters with those which are not. The combination of our NH3 and CCS observations with previous millimeter, sub-millimeter, and Spitzer data available for this cloud enable us both to determine core properties precisely and to accurately classify cores as starless or protostellar. The properties of cores in different cluster environments and before-and-after star formation provide important constraints on simulations of star-formation, particularly under the paradigm that the essence of star formation is set by the turbulent formation of prestellar cores. We separate the influence of stellar content from that of cluster environment and find that cores within clusters have (1) higher kinetic temperatures and (2) lower fractional abundances of CCS and NH3. Cores associated with protostars have (1) slightly higher kinetic temperatures (2) higher NH3 excitation temperatures), (3) are at higher column density, have (4) slightly more non-thermal/turbulent NH3 linewidths, have (5) higher masses and have (6) lower fractional abundance of CCS. We find that neither cluster environment nor protostellar content makes a significant difference to the dynamical state of cores as estimated by the virial parameter -- most cores in each category are gravitationally bound. Overall, cluster environment and protostellar content have a smaller influence on the properties of the cores than is typically assumed, and the variation within categories is larger than the differences between categories.