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
Kids can do it, and then they'll feel like they're a big deal, unless they're over 12, in which case they'll say "yeah whatever".
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