Low-lying equilibrium geometric structures of NanMg (n=1-12) clusters obtained by an all-electron linear combination of atomic orbital approach, within spin-polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three-parameter hybrid generalized gradient approximation (GGA) due to Becke-Lee-Yang-Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground-state structures within the GGA. It is observed that for clusters with n <9, symmetric structures with the magnesium atom occupying the internal position are higher in energy (typically by less than 1 eV) than those where Mg occupies a peripheral position. It is found that the relative ordering of the isomers is influenced by the nonlocal exchange-correlation effects for small clusters. Generalized gradient approximation extends bond lengths and widens the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), as compared to the LSDA gap. The odd-even oscillations in the dissociation energy, the second differences in energy, the HOMO-LUMO gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energetics clearly shows the Na6Mg cluster to be endowed with special stability, which occurs because of an electronic shell closure.