I investigated the structural and electronic properties of both NanC60 and LinC60 (n <= 12) clusters in the framework of density-functional theory. The behavior of the alkali atoms over the C-60 surface is analyzed. The hypotheses for either an homogeneous coating of the C-60 surface by the alkali atoms or the growth of an alkali droplet not wetting the fullerene surface are discussed. Lithium atoms are found to coat homogeneously the fullerene on the C-60 surface via pentagonal sites, contrary to sodium atoms, which prefer to form 4-atom islands on the surface. The charge transfer, the energetics, and the dipole moments are discussed in relation with available results. The adsorption of alkali atoms on the C-60 surface considerably enhances the capacity of C-60 to accept electrons. The arrangement of lithium atoms seems more favorable for the hydrogen storage than that of sodium atoms.