Even today in our Galaxy, stars form from gas cores in a variety of environments, which may affect the properties of the resulting star and planetary systems. Here, we study the role of pressure, parameterized via ambient clump mass surface density, on protostellar evolution and appearance, focusing on low-mass Sun-like stars and considering a range of conditions from relatively low pressure filaments in Taurus, to intermediate pressures of cluster-forming clumps like the Orion Nebula Cluster, to very high pressures that may be found in the densest infrared dark clouds or in the Galactic center. We present unified analytic and numerical models for the collapse of prestellar cores, accretion disks, protostellar evolution, and bipolar outflows, coupled with radiative transfer calculations and a simple astrochemical model to predict CO gas-phase abundances. Prestellar cores in high-pressure environments are smaller and denser and thus collapse with higher accretion rates and efficiencies, resulting in higher luminosity protostars with more powerful outflows. The protostellar envelope is heated to warmer temperatures, affecting infrared morphologies (and thus classification) and astrochemical processes like CO depletion onto dust grain ice mantles (and thus CO morphologies). These results have general implications for star and planet formation, especially via their effect on astrochemical and dust grain evolution during infall to and through protostellar accretion disks.