Another important issue of approximate calculations is that the choice of gauge for the representation of the electric dipole perturbation leads to numerically different results, contrary to a hypothetical exact calculation. Furthermore, in the length gauge (LG) the OR is origin dependent while in the velocity gauge (VG) the OR has a spurious static limit. These are both unphysical artifacts due to the incompleteness of the basis set and of the electron correlation treatment in practical simulations. The origin dependence of LG calculations can be removed in variational methods using London orbitals, also known as gauge including atomic orbitals (GIAOs), at the cost of considerably more complicated equations and computer codes. Additionally, this approach cannot be used with standard CC methods, unless one employs uncommon orbital optimization techniques. Recently, our group has introduced an approach to obtain origin invariant LG results, LG(OI), without the need of GI-AOs so that it can be equally used with variational and non-variational methods. To obtain meaningful results with VG, one needs to calculate the spurious static term explicitly and subtract it out, an approach called modified VG (MVG). Despite all of the work mentioned above, it is not yet clear what choice of gauge, level of theory, and basis set is optimal for OR calculations. The main obstacle to such a determination has been the inability to perform a uniform comparison between choices of gauge and basis sets across variational and non-variational methods due to the unresolved issue of the origin dependence of standard LG calculations (before the development of the LG(OI) approach). Another problem is that a direct comparison with experimental data is difficult for this sensitive molecular property. On the one hand, simulations are not yet able to reliably account for solvation effects, vibrational effects are typically introduced only through approximate perturbative treatments, and proper averaging of multiple conformers of the same enantiomer with opposite OR sign requires very accurate relative energy calculations. On the other hand, experimental measurements of rigid chiral molecules in the gas phase (which would sidestep some of the above simulation limitations, i.e., conformational averaging and solvation effects) are very limited due to the low volatility of these compounds and the overall small signal. In this work, we address a number of these issues by performing a thorough analysis of the basis set dependence in approximate calculations of optical rotation using different choices of gauge. We use an extensive set of chiral molecules (50 at DFT level and 17 at CCSD level) to test how OR calculations approach the complete basis set (CBS) limit with the LG (including GIAOs for DFT), LG(OI), and MVG schemes. The calculations are performed with the aug-cc-pVζZ series up to ζ = Q followed by an extrapolation to the CBS limit, which provide a consistent improvement of the basis set description. We investigate the convergence towards the CBS limit for each choice of gauge within each method, the convergence towards gauge invariance for each method, and a comparison between methods at the CBS limit. Thus, we can draw important conclusions on the effect of basis set and electron correlation incompleteness for a given choice of gauge and model chemistry. We also attempt a limited comparison with experimental data for a subset of 5 rigid molecules for which experimental data in the gas phase are available.