I have used NEMA 17 motors on small cnc machines for all the axis without issue. For these motors I am using single start 8mm screws that work fine.
You have not given much information about you Z axis setup. I think a single start screw for NEMA 17 motors. You wont be able to put much weight on it. Some type of rotary is about all it will be able to handle. See my KReduCNC build here:
KReduCNC Introduction — Kronos Robotics