Use oil based paint with a brush.
As a furniture maker, I prefer oil over latex, better for the wood and holds up better. More consistent with furniture finishes. I work in a different realm of quality.
Plus it doesn't need a top coat or sealer.
No need to use oil based paint. I always use acrylic latex paint. Even mix my own custom colors. Lightly sand with 220 grit sandpaper to remove any shine. Wipe clean with a damp cloth. Prime with Kilz primer. Then paint your color. Seal with three coats of a water based polyurethane.
Take off the doors and any hardware. Sand with 100 grit sandpaper to rough up surface a little. Wipe down with vinegar and hot water; dry thoroughly. If you don't want to prime, use a chalk paint product (several coats) and seal with wax or polyurethane.