Do you want the machine to actually move the part or do that yourself?
If it were mine i would be looking at some type of linear motion - a beam with a sliding member on it connected to a belt maybe, the belt would be driven by a stepper motor for ease of build, once calibrated as to the position of the moving part which also has an end-stop on it, you just slide the metal in tell it to go to the first stop, push your stock up against the end-stop, punch, the punch process would trigger the next index move, you then slide material against stop, punch, repeat.
Its just an indexing end-stop, would only need one axis, could possibly be done with a PLC, but Mach would allow you to load files with preset stop positions in it - just load file press start and throw the metal at it all day.

Or if you want the machine to pull the metal in, then you need a little more power maybe, plus add an air gripper to the indexing stop, now you can just load a bar of stock, press run and watch. Naturally, what happens when the punch jams or takes a dump or whatever has to be dealt with too

And you will certainly want two-hand start buttons for safety.
Nice little project
