The high XMM-Newton throughput allows a detailed investigation of the spatial, spectral and variability properties of the extended and point source emission of the starburst galaxy NGC 253 simultaneously. We characterize the brightest sources by their hardness ratios, detect a bright X-ray transient, and show the spectrum and light curve of the brightest point source, most likely a black-hole X-ray binary. The unresolved emission of two disk regions can be modeled by two thin thermal plasma components of 0.13 and 0.4 keV plus residual harder emission, with the lower temperature component originating from above the disk, the nuclear spectrum by a three temperature plasma (~0.6, 0.9, and 6 keV) with the higher temperatures increasingly absorbed. The high temperature component most likely originates from the starburst nucleus. No non-thermal component, that would point at a significant contribution from an active nucleus (AGN), is needed. Assuming that type IIa supernova remnants (SNRs) are mostly responsible for the E>4 keV emission, the detection with EPIC of the 6.7 keV line allows us to estimate a supernova rate within the nuclear starburst of 0.2 yr^-1. RGS spectra and EPIC images reveal that the limb-brightening of the plume is mostly seen in higher ionization emission lines, while in the lower ionization lines, and below 0.5 keV, the plume is more homogeneously structured. (abridged)