Stepper or Servo?

steppers move a fixed fraction of a revolution with each pulse, if you gear them down enough you can get some fairly decent resolution but then you have all the slop in the gear train to deal with. not an ideal solution.

a better solution would be a servo. servos have a feedback mechanism that allows the controller to know where the shaft position is at all times and can adjust it with near infinite resolution.

There are two forms of feedback mechanisms for servos, encoders, which like steppers have discrete "steps" in their output. they also do not know their absolute position at startup, they have to turn a full revolution before they are oriented properly usually. this can be a problem if there are power outages and the machine forgets where it is in the cycle. The other feedback mechanism are resolvers which are essentially four quadrant variable transformers. They do not have the problem of losing their position when power is lost, but they don't have QUITE the angular resolution that encoders do but they are good enough for most things. You could combine the two, but most people don't. there are modified encoder systems that attempt to deal with the loss of position info in various ways with various levels of success. but there is nothing standardized about it.

I helped to design a similar punch for stainless strip using servo systems from Baldor. (The punch head itself was also servo controlled and didn't use a flywheel. It brute forced itself through the workpiece. That way we could control the punch speed throughout the cycle.) the Baldor equipment was dead simple to specify and use, but Rockwell Automation is not bad either. Most systems out there are getting pretty simple to use nowadays.