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Using scanning tunneling microscopy, reflection high energy diffraction and magnetic optical Kerr effect measurements, growth mode and the magnetic properties of epitaxial Co films on Si(111) with epitaxial Cu(111) buffer layers of various thicknesses have been studied. The strained 3.5-monolayer-thick Cu/Si(111) film has been found to be an optimal buffer, in which case an almost ideal layer-by-layer like growth of Co is observed up to six Co monolayers, due to a negligible lattice mismatch. The coercivity of Co films grown in this layer-by-layer like fashion has been determined to be about 10 Oe, testifying to the high quality of the formed Co film and Co/Cu interface. Changeover of the Co film growth mode from layer-by-layer like to multilayer has been found to result in the transition of the film magnetic properties from isotropic to markedly uniaxially anisotropic.