Basically speed and vibration are the right answers.
Speed: the more speed stable, the less 'shimmer' in the soundstage- the more it soundstages like tape. This is because the arm does not oscillate over the position of the stylus as it tracks the groove due to variation in skating forces as the LP rotation speed changes.
Vibration: there are several aspects
1) the platter pad has to control resonance in the LP without imparting any editorial of its own. To do this it has to be no harder or softer than the LP, but have the ability to absorb vibration.
2) the platter has to be dead such that you can hit it while the LP is playing and not hear anything in the playback. If you can hear something, its imparting its own signature.
3) the plinth must be dead also and here's a big factor: it must have absolutely rigid coupling between the mount for the platter bearing and that of the tone arm. If there is any flex or its not dead enough, the patter bearing and the base of the arm may be vibrating in completely different planes and different frequencies depending on the source of the vibration.
Turntables are all over the map on this last one; some are very good and some even have separate mounts that are entirely independent of the plinth (the latter demonstrating a misunderstanding of the requirements of proper playback)! Any difference in vibration between the platter surface and the locus of the cartridge in the arm will be interpreted by the pickup as a coloration.
That is why turntables can sound so different!
