We investigate the star-forming main sequence of the host galaxies of a large, well-defined sample of 453 redshift ~0.3 quasars with previously available star formation rates by deriving stellar masses from modeling their broadband (grizy) spectral energy distribution. We perform two-dimensional, simultaneous, multi-filter decomposition of Pan-STARRS1 3{pi} Steradian Survey images to disentangle the active galactic nucleus (AGN) from its host galaxy, by explicitly considering, for the first time, the wavelength variation of galaxy structures. We quantify the Sersic profiles and sizes of the host galaxies from mock AGNs generated from both real and idealized galaxies. Detailed morphological classifications of the calibration galaxy sample using Hubble Space Telescope images enable us to estimate crude morphological types of the quasars. Although the majority (~60%) of the quasars are hosted by bulge-dominated, early-type galaxies, a substantial fraction (~40%) reside in disk-dominated, late-type galaxies, suggesting that at least in these systems major mergers have not played a significant role in regulating their AGN activity, in agreement with recent simulations and observations of nearby quasars. The vast majority (~90%) of the quasars have star formation rates that place them on or above the galaxy star-forming main sequence, with more rapidly accreting AGNs displaced further above the main sequence. Quasar host galaxies generally follow the stellar mass-size relation defined by inactive galaxies, both for late-type and early-type systems, but roughly 1/3 of the population has smaller sizes at a given stellar mass, reminiscent of compact star-forming galaxies at higher redshift.