Sanding after the first coat

Paint: Use interior semi-gloss latex house paint...

A word about primer: Primer is designed to help paint stick to an impervious surface or to join layers of dissimilar paints. In this application, the first coat of paint soaks right into the wood and fills the grain - you could do that with primer, but its job of being an interface between different materials doesn’t apply here. In this application, primer just adds steps and expense. I don’t use it under exterior colors, but I do one-coat and sand the interior walls and ceilings before assembly, and primer is a good choice for that.

Paint the parts the first coat. The first coat mostly soaks into the wood, filling and reinforcing the grain so the sanding step clips off the fibers and leaves the surface smooth. Resist sanding before painting - it will leave the surface fuzzy and make a smooth finish harder to achieve. The quality of your final finish is dependent on the quality of the sanding after the first coat. Do not go back to re-paint just because the paint has soaked in. Just a bit of paint left on the surface tells you you have put on enough to saturate the grain, which is the right amount. More paint than that will only make sanding harder.

Glue doesn’t stick to paint. Avoid painting edges, grooves, and areas that will be glued.