We present the results of a photometric redshift analysis designed to identify z>6 galaxies from the near-IR HST imaging in three deep fields (HUDF, HUDF09-2 & ERS). By adopting a rigorous set of criteria for rejecting low-z interlopers, and by employing a deconfusion technique to allow the available IRAC imaging to be included in the candidate selection process, we have derived a robust sample of 70 Lyman-break galaxies (LBGs) spanning the redshift range 6.0<z<8.7. Based on our final sample we investigate the distribution of UV spectral slopes (beta), finding a variance-weighted mean value of <beta>=-2.05 +/- 0.09 which, contrary to some previous results, is not significantly bluer than displayed by lower-redshift starburst galaxies. We confirm the correlation between UV luminosity and stellar mass reported elsewhere, but based on fitting galaxy templates featuring a range of star-formation histories, metallicities and reddening we find that, at z>=6, the range in mass-to-light ratio (M*/L_UV) at a given UV luminosity could span a factor of ~50. Focusing on a sub-sample of twenty-one candidates with IRAC detections at 3.6-microns we find that L* LBGs at z~6.5 have a median stellar mass of M* = (2.1 +/- 1.1) x 10^9 Msun and a median specific star-formation rate of 1.9 +/- 0.8 Gyr^-1. Using the same sub-sample we have investigated the influence of nebular continuum and line emission, finding that for the majority of candidates (16 out of 21) the best-fitting stellar-mass estimates are reduced by less than a factor of 2.5. Finally, a detailed comparison of our final sample with the results of previous studies suggests that, at faint magnitudes, several high-redshift galaxy samples in the literature are significantly contaminated by low-redshift interlopers (abridged).