This paper presents a large spectral line and continuum survey of eight deeply embedded, low-mass protostellar cores using the SMA. High-excitation line emission from 11 molecular species originating in warm and dense gas has been imaged at high angular resolution (1''-3'', typically 200-600 AU) together with continuum emission at 230 GHz (1.3 mm) and 345 GHz (0.8 mm). Compact continuum emission is observed for all sources, which likely originates in marginally optically thick circumstellar disks, with typical lower limits to their masses of 0.1 M (1%-10% of the masses of their envelopes) and a dust opacity law, κ_ν ν^β, with β ≈ 1. Prominent collimated outflows are present in CO 2-1 observations in all sources. The most diffuse outflows are found in the sources with the lowest ratios of disk to envelope mass, and it is suggested that these sources are in a phase where accretion of matter from the envelope has almost finished and the remainder of the envelope material is being dispersed by the outflows. Other characteristic dynamical signatures are inverse P Cygni profiles indicative of infalling motions seen in the ¹³CO 2-1 lines toward NGC 1333 IRAS 4A and NGC 1333 IRAS 4B. Outflow-induced shocks are present on all scales in the protostellar environments and are most clearly traced by the emission of CH₃OH in NGC 1333 IRAS 4A and NGC 1333 IRAS 4B. These observations suggest that the emission of CH₃OH and H₂CO from these proposed ``hot corinos'' is related to the shocks caused by the protostellar outflows. Only one source, NGC 1333 IRAS 2A, has evidence for hot, compact CH₃OH emission coincident with the embedded protostar.