A systematic investigation has been undertaken on the basis set requirements for the calculation of optical tensors. In this first of a series of two papers we present a comparison of the performance of various basis sets for the calculation of the Raman and Raman optical activity (ROA) scattering tensor. We show that it is possible to obtain results in excellent qualitative and in reasonable quantitative agreement with those from complex sets by highly rarefied sets provided the vibrational problem is solved in a separate calculation. It is shown that, for hydrogen-containing molecules, a basic requirement for the effectiveness of rarefied basis sets is the proper description of gradients of electronic tensors on these atoms and that this can only be achieved by the inclusion of moderately diffuse p-type functions on these atoms. In addition, the correct rendering of the Raman and ROA tensor for main atom-hydrogen and main atom-deuterium stretching vibrations requires a layer of diffuse functions with valence angular momentum quantum numbers on all atoms. A split valence shell description matters similarly for most other molecular vibrations. The proper description of the core electrons, on the other hand, is of utter unimportance. Questions which arise for rarefied basis sets, such as balance and gauge origin dependence of the optical activity tensor, will be addressed in a second paper.