It has been recently shown that under pressure trilayer Ruddlesden-Popper nickelate La4Ni3O10 (LNO) becomes superconducting below a critical temperature ≈20 K, in addition to the infinite-layer and bilayer systems. Motivated by this observation, we explore the effects of electron correlations on its electronic structure and magnetic properties using the advanced density functional theory plus dynamical mean-field theory approach. Our results for the normal-state electronic structure and correlation effects in LNO show much in common with the infinite-layer and bilayer nickelates, with remarkable site- and orbital-dependent renormalizations of the Ni 3d bands and notable incoherence of the Ni d3z2-r2 states, caused by correlation effects. Our analysis of the Fermi surface and magnetic correlations suggests the emergence of competing spin and charge stripe states, implying the importance of in-plane spin fluctuations to explain superconductivity in this material.