The power supply and output stage are vitally important as if they cannot deliver the voltage and current that the speaker needs, then you are already on the backfoot.
Slew rate was a problem in the 70s (It caused transient intermodulation distortion which gave amps a brittle sound) however once it was recognised, amps were designed to mitigate this and it has not been a problem since.
As to the pre-amp part, low noise, low distortion and quality components play a big part, no matter the design used, but all this costs money so the cheaper amps/receivers have to make compromises, hence you really need to hear the combination to make sure they all match.
As the ATCs are designed to be as neutral as possible then providing the amp has got the oomph (Which costs money) to drive them you will also get a neutral sound. (Most of the Marantz amps give a slightly warmer sound rather than a neutral sound so can make poor masters sound a bit more pleasant)
Bill