for the putty, I usually use this

Impra wood filler

so that the putty results from the screw marks are the maximum, I usually do the putty process up to 3 times with a thick putty until the screw marks are completely flush with the wood surface, then I continue by caulking the entire surface the project to be painted using putty which I mixed with a solution (oil or thinner), then sanded it using fine sandpaper (240,400) for maximum results.
And for the paint, I stirred a little liquid in the first layer, and then I sanded it with fine used sandpaper and sanding it shouldn't be pressed too hard it just floats and I do that step again after the second layer and so on until I feel the paint results are maximized, I hope my explanation can help and thank you for asking...