Comprehensive computer simulation has been used to investigate an impact of various possible structure modifications of the 1.3-mu m oxide-confined GaAs-based GaInNAs quantum-well (QW) vertical-cavity surface-emission diode lasers (VCSELs) on their operation. In particular, an influence on various physical phenomena crucial for the VCSEL operation and leading to some beneficial improvements in the VCSEL performance, i.e. detuning of the cavity mode with respect to the maximal optical gain, sizes and localizations of one or two the oxide apertures, sizes of the possible proton implantation and the step-like active-region QW structure, has been examined. A possibility to achieve the efficient 1.3-mu m radiation, to reduce the VCSEL threshold current, to improve the VCSEL operation at elevated temperatures and to preserve the single-fundamental-mode operation are used as criteria of the desirable VCSEL performance. It has been concluded from our analysis, that the best performance of the 20-mu m diameter VCSEL may be expected in its structure in which the proper detuning of the cavity mode towards longer wavelengths, the proper step-like active-region QW structure as well as the proper separate confinements of the optical field with the oxide aperture and the current funneling with the proton implantation are simultaneously applied.