We have theoretically investigated the combined fundamental-mode and polarization selection in 850-nm oxide-confined vertical-cavity surface-emitting lasers (VCSELs) using a locally etched sub-wavelength surface grating. The physical mechanisms behind the selection are, first, the strongly polarization sensitive effective refractive index of the volume occupied by the grating structure, and second, the dramatic change of the reflectivity of a multi-layer Bragg mirror that can occur by simply changing the refractive index of the outermost layer. For a VCSEL cavity this layer is the surface layer and its refractive index is changed by the introduction of the sub-wavelength grating; in this case the grating leads to a higher reflectivity for the desired polarization. By localizing the surface grating area to a carefully chosen region near the optical axis it is therefore possible to ensure that the fundamental mode experiences a high reflectivity, or low cavity loss, while other modes experience more of the low-reflectance region of the peripheral part of the Bragg mirror and thus suffer higher loss. Cold-cavity calculations on a VCSEL with oxide aperture and grating region diameters of 4.5 microm and 2.5 microm, respectively, indicate that a loss difference of ~20 cm(-1) between the fundamental mode and the first higher order mode can be obtained simultaneously with an orthogonal polarization mode discrimination of >15 cm-1. Based on previous experience, these values should enable robust single-mode operation with only the desired polarization orientation. What is also important, for the lasing mode the introduction of a sub-wavelength grating has no detrimental effect, so its characteristics, such as threshold current, slope efficiency, and far-field profile are unaffected. Moreover, since the effective index is a result of an averaging over several sub-wavelength grating periods, it is fairly insensitive to the detailed shape of the grating grooves, which should relax the fabrication tolerances.