We present a homogeneous and 92 % complete dataset of optical nuclear spectra for the 113 3CR radio sources with redshifts < 0.3, obtained with the Telescopio Nazionale Galileo. For these sources we could obtain uniform and uninterrupted coverage of the key spectroscopic optical diagnostics. The observed sample, including powerful classical FR II radio-galaxies and FR I, together spanning four orders of magnitude in radio-luminosity, provides a broad representation of the spectroscopic properties of radio galaxies. In this first paper we present an atlas of the spectra obtained, provide measurements of the diagnostic emission line ratios, and identify active nuclei with broad line emission. These data will be used in follow-up papers to address the connection between the optical spectral characteristics and the multiwavelength properties of the sample.