Context. Planetary nebulae (PNe) around Wolf-Rayet [WR] central stars ([WR]PNe) constitute a particular photoionized nebula class that represents about 10% of the PNe with classified central stars. Aims: We analyse deep high-resolution spectrophotometric data of 12 [WR] PNe. This sample of [WR]PNe represents the most extensive analysed so far, at such high spectral resolution. We aim to select the optimal physical conditions in the nebulae to be used in ionic abundance calculations that will be presented in a forthcoming paper. Methods: We acquired spectra at Las Campanas Observatory with the 6.5-m telescope and the Magellan Inamori Kyocera (MIKE) spectrograph, covering a wavelength range from 3350 Å to 9400 Å. The spectra were exposed deep enough to detect, with signal-to-noise ratio higher than three, the weak optical recombination lines (ORLs) of O ii, C ii, and other species. We detect and identify about 2980 emission lines, which, to date, is the most complete set of spectrophotometric data published for this type of objects. From our deep data, numerous diagnostic line ratios for Te and ne are determined from collisionally excited lines (CELs), ORLs, and continuum measurements (H i Paschen continuum in particular). Results: Densities are closely described by the average of all determined values for objects with ne < 104 cm-3, and by ne([Cl iii]) for the densest objects. For some objects, ne([Ar iv]) is adopted as the characteristic density of the high ionization zone. For Te, we adopt a three-zone ionization scheme, where the low ionization zone is characterised by Te([N ii]), the medium ionization zone by Te([O iii]), and the highest ionization one by Te([Ar iv]) when available. We compute Te from the H i Paschen discontinuity and from He i lines. For each object, Te(H i) is, in general, consistent with Te derived from CELs, although it has a very large error. Values of Te(He i) are systematically lower than the Te derived from CELs. When comparing Te(H i) and Te(He i) it is unclear whether the behaviour of both temperatures agrees with the predictions of the temperature fluctuations paradigm, owing to the large errors in Te(H i). We do not find any evidence of low-temperature, high-density clumps in our [WR]PNe from the analysis of faint O ii and N ii plasma diagnostics, although uncertainties dominate the observed line ratios in most objects. The behaviour of Te([O iii])/Te([N ii]), which is smaller for high ionization degrees, can be reproduced by a set of combined matter-bounded and radiation-bounded models, although, for the smallest temperature ratios, a too high metallicity seem to be required. Based on data obtained at Las Campanas Observatory, Carnegie Institution.Full Table 3 and Fig. 3 are available in electronic form at http://www.aanda.org