VLT/FORS spectroscopy and 2MASS near-infrared photometry, together with previously known data, have been used to establish the membership and the properties of a sample of low-mass candidate members of the sigma Orionis cluster with masses spanning from 1 Msun down to about 0.013 Msun (i.e., deuterium-burning mass limit). We have observed K-band infrared excess and remarkably intense H(alpha) emission in various cluster members, which, in addition to the previously detected forbidden emision lines and the presence of LiI in absorption at 6708 A, have allowed us to tentatively classify sigma Orionis members as classical or weak-line TTauri stars and substellar analogs. Variability of the H(alpha) line has been investigated and detected in some objects. Based on the K-band infrared excesses and the intensity of H(alpha) emission, we estimate that the minimum disk frequency of the sigma Orionis low-mass population is in the range 5-12%.