<p>When trying to print parts that should contain certain sized holes, e.g. for screws, how to achieve that they are sized correctly?</p>

<p>Is it possible to calibrate the printer perfectly, so it prints holes correctly sizes in all common sizes (e.g. starting at 2mm diameter)? Or is it better to design the holes larger or print prototypes and increase the sizes according to the real prints?</p>

The reason holes come out undersized is generally the slicer
, so calibrating the printer itself cannot solve the issue (without making other things worse). The output of the printer is exactly what it should be, given the G-code provided to it. It's just that the G-code does not represent the hole diameter correctly.
It would be best to simply account for the deviation in your design, or simply drill out undersized holes to the correct diameter.