We present an extensive numerical study of the ferromagnetic Kondo lattice model with quantum mechanical S=3∕2 core spins. We treat one orbital per site in one dimension using the density-matrix renormalization group and include on-site Coulomb repulsion between the electrons. We examine parameters relevant to manganites, treating the range of low to intermediate doping, 0≲xtextless0.5. In particular, we investigate whether quantum fluctuations favor phase separation over the ferromagnetic polarons observed in a model with classical core spins. We obtain very good agreement of the quantum model with previous results for the classical model, finding separated polarons, which are repulsive at short distance for finite t2g superexchange J′. Taking on-site Coulomb repulsion into account, we observe phase separation for small but finite superexchange J′, whereas for larger J′, polarons are favored in accordance with simple energy considerations previously applied to classical spins. We discuss the interpretation of compressibilities and present a phase diagram with respect to doping and the t2g superexchange parameter J′ with and without Coulomb repulsion.