Molecular lines are powerful diagnostics of the physical and chemical properties of the interstellar medium (ISM). These ISM properties, which affect future star formation, are expected to differ in starburst galaxies from those of more quiescent galaxies. We investigate the ISM properties in the central molecular zone of the nearby starburst galaxy NGC 253 using the ultrawide millimeter spectral scan survey from the Atacama Large Millimeter/submillimeter Array Large Program ALCHEMI. We present an atlas of velocity-integrated images at a 1.″6 resolution of 148 unblended transitions from 44 species, including the first extragalactic detection of HCNH+ and the first interferometric images of C3H+, NO, and HCS+. We conduct a principal component analysis (PCA) on these images to extract correlated chemical species and to identify key groups of diagnostic transitions. To the best of our knowledge, our data set is currently the largest astronomical set of molecular lines to which PCA has been applied. The PCA can categorize transitions coming from different physical components in NGC 253 such as (i) young starburst tracers characterized by high-excitation transitions of HC3N and complex organic molecules versus tracers of on-going star formation (radio recombination lines) and high-excitation transitions of CCH and CN tracing photodissociation regions, (ii) tracers of cloud-collision-induced shocks (low-excitation transitions of CH3OH, HNCO, HOCO+, and OCS) versus shocks from star formation-induced outflows (high-excitation transitions of SiO), as well as (iii) outflows showing emission from HOC+, CCH, H3O+, CO isotopologues, HCN, HCO+, CS, and CN. Our findings show these intensities vary with galactic dynamics, star formation activities, and stellar feedback.