Context. The Tarantula region in the Large Magellanic Cloud contains the richest population of spatially resolved massive O-type stars known so far. This unmatched sample offers an opportunity to test models describing their main-sequence evolution and massloss properties. Aims. Using ground-based optical spectroscopy obtained in the framework of the VLT-FLAMES Tarantula Survey (VFTS), we aim to determine stellar, photospheric and wind properties of 72 presumably single O-type giants, bright giants and supergiants and to confront them with predictions of stellar evolution and of line-driven mass-loss theories. Methods. We apply an automated method for quantitative spectroscopic analysis of O stars combining the non-LTE stellar atmosphere model fastwind with the genetic fitting algorithm pikaia to determine the following stellar properties: effective temperature, surface gravity, mass-loss rate, helium abundance, and projected rotational velocity. The latter has been constrained without taking into account the contribution from macro-turbulent motions to the line broadening.Results. We present empirical effective temperature versus spectral subtype calibrations at LMC-metallicity for giants and supergiants. The calibration for giants shows a +1kK offset compared to similar Galactic calibrations; a shift of the same magnitude has been reported for dwarfs. The supergiant calibrations, though only based on a handful of stars, do not seem to indicate such an offset. The presence of a strong upturn at spectral type O3 and earlier can also not be confirmed by our data. In the spectroscopic and classical Hertzsprung-Russell diagrams, our sample O stars are found to occupy the region predicted to be the core hydrogen-burning phase by Brott et al. (2011) andKöhler et al. (2015). For stars initially more massive than approximately 60 M ⊙ , the giant phase already appears relatively early on in the evolution; the supergiant phase develops later. Bright giants, however, are not systematically positioned between giants and supergiants at M init ∼ > 25 M ⊙ . At masses below 60 M ⊙ , the dwarf phase clearly precedes the giant and supergiant phases; however this behavior seems to break down at M init ∼ < 18 M ⊙ . Here, stars classified as late O III and II stars occupy the region where O9.5-9.7 V stars are expected, but where few such late O V stars are actually seen. Though we can not exclude that these stars represent a physically distinct group, this behaviour may reflect an intricacy in the luminosity classification at late O spectral subtype. Indeed, on the basis of a secondary classification criterion, the relative strength of Si iv to He i absorption lines, these stars would have been assigned a luminosity class IV or V. Except for five stars, the helium abundance of our sample stars is in agreement with the initial LMC composition. This outcome is independent of their projected spin rates. The aforementioned five stars present moderate projected rotational velocities (i.e., e sin i < 200 km s −1 ) and hence do no...