ballscrews are defined by their diameter and pitch. You will generally see numbers such as 1204 or 1610. The first 2 digits indicate the diameter (e.g. 16mm) and the second two indicate the lead (e.g. 10).
Ballscrews can be ground or rolled. Ground ball screws are generally better quality and will be more accurate (C0-C7 vs C6-C10). However, ground ballscrews are significantly more expensive than rolled Aliexpress variants. The standard ballscrew found on Aliexpress is a C7 grade and is adequate for the price.
https://www.hiwin.com/pdf/ballscrews.pdf
https://www.linearmotiontips.com/choose-end-fixity-conditions-screw-applications
https://ncalculators.com/mechanical/lead-screw-critical-speed-calculator.htm
1610/2010 is standard for the PrintNC. 1605 you need double the rotation to go the same distance. Stepper motors lose torque as their speed increases, a 1610 means we can stay in the right section of the curve for best motor performance and still have high speed rapids. The length depends on your desired dimensions.
Ballscrew lengths over 1500mm need to be 2010 to limit the whip created from spinning long unsupported rods at high speeds. At 1500mm, a 1610 ballscrew is at max rotation at 750rpm or 7500mm/min travel.
The Z-axis in V2.1 uses a 300mm 1204 ballscrew.
Rolled ballscrews are inexpensive and plentiful on AliExpress and are included in the PrintNC kit.
These are other sources: