The adsorption of Cs and Ba on Cu(111) is investigated by means of one- and two-photon photoemission experiments and theoretically by first-principles calculations. The spectral properties of these systems, induced by both surface and adatom states, are studied at submonolayer coverage through angle-resolved measurements. A coverage-dependent analysis is also exploited in the assignment of the observed electronic states. The comparison with ab initio calculations allows identification of all the spectral features induced by Cs and Ba chemisorption. The theoretical analysis concerns the limiting single adatom case, treated in an embedding approach with a one-dimensional potential for the surface. The agreement between the calculated density of states and the experimental spectra confirms that the model substrate retains all the relevant physics entering in the adsorption process. The differences between the electronic structures of Cs and Ba on the Cu(111) surface can be attributed to the group-dependent screening of the core potentials as manifested by the ionic radii and ionization potentials (alkali vs alkaline earth).