Painting

[Semon]

I built a vanity for the bathroom and my wife wants to be white.
I primed it and used wall paint for it with a airless sprayer it came out textured not smooth so I thinned it down and tried a my air sprayer and it helped with the texturing but it wasn't putting out enough paint to cover rite.
What is the best way to paint wood?
And I think that a brush will leave stroke marks.