With the advent of large spectroscopic surveys, automated stellar parameter determination has become commonplace. Nevertheless, spectral classification still offers a quick and useful alternative for obtaining parameter estimates for large samples of spectra of varying quality. We present a new atlas of stellar spectra covering the B-type range, with the intention of providing detailed classification criteria valid for modern spectra and improving the grid of reliable standards. This new grid will be used in future works to provide classification criteria beyond the classical classification range and addressing, in particular, the use of Gaia/RVS spectra. We analysed historical standards by means of multiple high-resolution spectra, marking out problematic cases and complementing the grid with a new set of reliable comparators. We then elaborated on a new set of classification criteria based on high-quality R=4000 spectra. Our new classification grid is much thicker than any previous set of standards, presenting a high degree of self-consistency. Although it is based entirely on morphological criteria, the grid demonstrates a much better correlation with different physical parameters. The new grid can be used to study classification criteria in other spectral ranges, providing a valuable tool for the study of B-type stars that covers a very wide range of temperatures, luminosities, and stellar masses. The very process of classification also offers valuable insights into stellar evolution.