That's right about stepper motors, for this application they're not good you risk modulating a pattern on the groove spiral. What i will use is a servo motor with analogue feedback. The motor geared a high ratio to the leadscrew.
In this application the feedrate is continuously variable, louder music has wider grooves on the disc you need to compensate for this. It's a balancing act between loudness, time, and quality
So i need to read up on how to work out leadscrews and their gearing, if anyone got any links etc
Thanks