Dwarf spheroidal (dSph) galaxies are prime targets for present and future gamma-ray telescopes hunting for indirect signals of particle dark matter. The interpretation of the data requires careful assessment of their dark matter content in order to derive robust constraints on candidate relic particles. Here, we use an optimised spherical Jeans analysis to reconstruct the `astrophysical factor' for both annihilating and decaying dark matter in 21 known dSphs. Improvements with respect to previous works are: (i) the use of more flexible luminosity and anisotropy profiles to minimise biases, (ii) the use of weak priors tailored on extensive sets of contamination-free mock data to improve the confidence intervals, (iii) systematic cross-checks of binned and unbinned analyses on mock and real data, and (iv) the use of mock data including stellar contamination to test the impact on reconstructed signals. Our analysis provides updated values for the dark matter content of 8 `classical' and 13 `ultrafaint' dSphs, with the quoted uncertainties directly linked to the sample size; the more flexible parametrisation we use results in changes compared to previous calculations. This translates into our ranking of potentially-brightest and most robust targets---viz., Ursa Minor, Draco, Sculptor---, and of the more promising, but uncertain targets---viz., Ursa Major 2, Coma---for annihilating dark matter. Our analysis of Segue 1 is extremely sensitive to whether we include or exclude a few marginal member stars, making this target one of the most uncertain. Our analysis illustrates challenges that will need to be addressed when inferring the dark matter content of new `ultrafaint' satellites that are beginning to be discovered in southern sky surveys. ; Comment: 19 pages, 14 figures, submitted to MNRAS. Supplementary material available on request