Depending on the precision of the 3D printer, the model can be printed directly without any further settings.
The zigzag pattern for infill has proven to be the most efficient.

The holes hold M3 screws very well, they cut the thread into the material themselves.
If the printer tends to overprint, simply drill the hole free again with a 3mm drill bit and place a M3 nut on the other side.

The model can also be easily scaled up for larger screws and projects. 
e.g. M3 -> M5: Print the model by 166.666 %.