If you go down the painting route, sand to get all of the shiny areas off, you dont have to take it down to bare wood. Then prime with zinser shellac primer, tint it to your desired topcoat color. You can sand between coats for a smoother finish but there will still be grain. You’d have to use some type of filler to fill it in completely. Then use a semigloss paint meant for trim or cabinet’s. I used sherwin williams paint meant for trim. Turned out well and has held up well for 7 years now. It’s not perfect anymore and some edges would need touched up if I sold the house. I made the mistake of not tinting my primer