We have employed a hierarchy of basis sets and computational techniques in order to approach the polarizability (alpha) of Zn(m), m = 2-20, in a systematic way. This procedure allows the proper approximate results to be selected and validated. More specifically, we have developed in a systematic way a series of basis sets that have been employed for the computation of the polarizability of the Zn atom. Comparison of the computed with the experimental and the best theoretical results allows us to comment on the quality of the basis sets, and to select some of the more successful ones in order to compute the polarizabilities of Zn(m), m = 2-20. We have employed a series of methods to take into account the correlation contribution. These include the following techniques: MP2, CC2, CCSD, CCSD(T), and DFT(B3LYP). We have used two effective core potentials, one small (3s2 3p6 3d10 4s2) and one large (4s2) core. The relativistic contribution to the properties is found to be significant. Thus we have studied in detail the relativistic effects on the polarizability of some small zinc clusters, by employing the Douglas-Kroll approximation in connection with the polarized basis sets developed by Kellö and Sadlej and the methods HF, CC2, and CCSD. Most of the polarizability values are static, but some frequency-dependent properties have also been computed in order to find out the difference between the dynamic and static ones. It is considered that the sharp changes of alpha(Zn(m))/m vs m may be correlated with the change of bonding, from van der Waals to covalent and finally to metallic bonding, in Zn(m). The present comprehensive study of the polarizabilities of Zn(m) includes a limited number of results for the first and second hyperpolarizability of some of the considered zinc clusters.