A method is presented to obtain well-equilibrated atactic polystyrene (aPS) samples for Molecular simulations. The method starts with equilibrating the polymer in the melt at length scales beyond the Kuhn length l(K), using end-bridging Monte Carlo techniques; at this level a (2:1)-coarse-grained description of aPS is being employed. Subsequently atomistic detail is reintroduced, and the sample is equilibrated at the smallest length scales as well. At length scales beyond Is the simulated polymer chain conformations fulfill the random-coil hypothesis of Flory, and C-infinity = 8.7 +/- 0.1 at 463 K. Eventually various glassy samples are created by subjecting the melt sample to different cooling rates. Pair correlations are in agreement with existing X-ray data, and the amount of dihedral angles in the trans (1) state agrees with NMR data. On the level of dyads, the conformations of racemic dyads agree well with existing NMR results. At the same time, meso dyads conformations do not agree: 65% of meso dyads is in the gt/tg state (NMR: 80%) 25% is in it state (NMR: < 10%). An attempt has been made to relate the observation in simulations, namely that an increase in cooling time causes an increase in yield stress, to effects of the cooling rate on the polymer structure.