I don't know why you wouldn't attempt covering the screw heads (& more).
Its easy and fun. I have both opinions of what primer is. My usual
solution is to gather any white paint(s) from anywhere - mis-match racks at
the store for a buck or three, leftovers, garbage picked, and mix them all
together. Unless its specific work, eg fine wood or metal, or stains,
sometimes requiring sanding between coats.
and if you are trying to achieve a color it can be faster to tint the primer
beforehand (with the final or other closer color paint) , its easier to get
from one shade to the other, or final color.
....and mix them all together first
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