Context. Sulfur chemistry is poorly understood in the process of low-mass star and planet formation, where the main carriers of sulfur in both the gas and the dust phase are still unknown. Furthermore, the chemical evolution of sulfur-bearing species is not fully understood given that simple S-bearing molecules, such as SO and SO2, are commonly seen in embedded Class 0/I sources but hardly detected in more evolved Class II disks. Despite the fact that simple S-bearing molecules are usually detected toward embedded sources, large surveys of S-bearing molecules with high angular resolution and sensitive observations are currently lacking. Aims. The goal of this work is to present an unbiased survey of simple sulfur-bearing species in protostars and provide new statistics on detection rates, emitting regions, and molecular column densities. In addition, we investigate the role of S-bearing molecules in accretion processes and the connection between (non-)detection of complex organic molecules (COMs) and S-related species. Methods. We present the observations of sulfur-bearing species (CS, SO,34SO, and SO2) that are part of the Perseus ALMA Chemical Survey (PEACHES). We analyzed a total of 50 Class 0/I sources with observations that have an average angular resolution of about 0″.6 (∼180 au) in ALMA band 6. Results. Class 0 sources show detection rates of 97% for CS, 86% for SO, 31% for 34SO, and 44% for SO2, while Class I sources present detection rates of 71% for CS, 57% for SO, 36% for 34SO, and 43% for SO2. When 34SO is detected, the SO/34SO ratio is lower than the canonical value of 22, suggesting optically thick emission, and the lowest values are found for those sources that are rich in COMs. When SO2 is detected, those sources that show CS and SO emission parallel to the outflow direction are usually very rich in COMs, while for sources where the CS and SO emission is perpendicular to the outflow direction, only a few or no COMs are detected. When CH3OH and SO2 are detected, the comparison between CH3OH and SO2 abundances shows a positive trend and CH3OH is between 10 and 100 times more abundant than SO2. The SO2 abundances toward the PEACHES sample are, on average, two orders of magnitude lower than values from the Ophiuchus star-forming region and comparable with sources in Taurus. Conclusions. The SO/34SO ratio seems to be a good tracer of the inner high-density envelope and it could be used in the future to infer the presence of multiple COMs. The detection of multiple COMs seems to be related to the presence of collimated outflows (seen in CS and SO emission), where a high column density of warm material is expected close to the protostar, and SO2 emission seems to trace the warm gas in those sources where CH3OH is also detected. The difference in SO2 abundances between different star-forming regions might indicate that the sulfur depletion in the gas-phase could depend on the external UV radiation toward the molecular cloud. Finally, the SO2 emission detected in different evolutionary stages seems to arise from different physical mechanisms: high column density of warm material in Class 0 sources, shocks in Class I/II, and exposure to UV radiation from the protostar in more evolved Class II disks.