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 Hα emission in various cluster members, which, in addition to the previously detected forbidden emision lines and the presence of Li I in absorption at 6708 Å, have allowed us to tentatively classify sigma Orionis members as classical or weak-line T Tauri stars and substellar analogs. Variability of the Hα line has been investigated and detected in some objects. Based on the K-band infrared excesses and the intensity of Hα emission, we estimate that the minimum disk frequency of the sigma Orionis low-mass population is in the range 5-12%. These observations were collected at the VLT of the European Southern Observatories. Table 2 is only available in electronic form at http://www.edpsciences.org