A wide variety of ab initio methods are used to study systematically the effects of electronic correlation on the charge density distribution, band structure, lattice parameters, phonon frequencies at the Brillouin zone center, and first-order elastic constants (C-ij) of Mg2Si. Two distinct atom-centered basis sets have been used: an all electron one, and another associated with core pseudopotentials. Various levels of approximation have been tested: (i) HF (Hartree-Fock-Roothaan) calculations with no correlation energy correction; (ii) Hartree-Fock plus a posteriori correlation energy correction estimated using various DFT (density functional theory) correlation functionals applied to the Hartree-Fock electronic density; (iii) DFT calculations with "exact" HF exchange and various DFT correlation functionals; (iv) "complete" DFT calculations in which both exchange and correlation are treated using a selection of exchange-correlation functionals. On the ground of a comparison of the numerous data, complemented by plotted band structure and electronic density maps,the advantages and drawbacks of the representation of correlation within the four levels of approximation are discussed. Special focus is placed on the need for including correlation in the calculation of properties related to derivatives of the electronic potential energy surface of the crystal (phonon frequencies) and to electronically excited states (band gap problem). Because of the peculiar partitions of exchange and correlation energies in DFT functionals, it is emphasized that the combination of HF exchange with DFT correlation functionals is inadequate and may even worsen the HF errors on dynamical quantities involving inner atomic displacements. In contrast, more satisfactory results are generally obtained carrying out complete exchange-correlation calculations.