You need to Clean the substrate first (TSP/degreaser), use a bonding primer and then I would recommend Sherwin Williams Emerald Urethanized trim paint. It has a longer upon time than most and is pretty easy to use. Semi Gloss is industry Standard. If you skip a step, like cleaning with TSP you may have issues down the road with peeling and chipping.
They are just pine trim boards. You can also use MDF trim boards. That's what I'll use next time. Cheaper and easier to cut smooth. I brought the doors home and did the boards so I wouldn't make noise and a mess in the apartment. Glued and then trim nailed. You can caulk around the sides to cover up any gaps. I'm going to do my own next summer since these have held up so well.
@Chris Mackinlay this is the process I use for just straight painting (no effects). Everyone has their own process but I have found this works best for me in terms of looks and durability. I only take jobs that are REAL wood, so this process isn’t applied to any other material. I also do aging/glazing etc and for that I use a different type of paint.
1. Remove doors and all hardware. You can clean the hardware with vinegar and water and reuse or get new. I have even repainted hardware by using a spray paint to prime, paint and seal.
2. Clean doors, cabinets and drawers with Krudcutter (a degreaser). I use a green scouring pad. Pay close attention to knob area as this has lots of grease and grime and will interfere with adhesion. Rinse and let dry.
3. Sand - I do not sand all the way down for painting. I usually use 120 grit and do a light sanding. Mainly knocking down the shine and hitting the knob area well. Some people use a deglosser, I just prefer to sand. Wipe everything down with damp cloth. Right before priming I wipe down with tack cloth.
4. Prime - I use a shellac based primer for 2 reasons. It has great adhesion and it prevents bleeding. I use zinnser but there are other brands. I follow instructions on drying and painting times. You may need to sand with 220 grit if you have bumps or rough areas after priming.
5. Paint - for straight paint, I use Valspar cabinet enamel. It has a good working time, self levels and self seals. I use a 4-6 inch nap roller and small brush. You can clean spray but that just isn’t my method. It is important to follow drying times as instructed on the can! I always do at least 2 light coats. You can lightly sand between coats with 220 grit if needed and wipe with damp lint free cloth and or tack cloth.
Someone mentioned chalk paint.... I do a lot of work with chalk paint because in my market aging cabinets is very popular. Just a note on chalk paint.... it must ALWAYS be sealed with a high performance sealer. It is very absorbent and will pick up stains like a boss if left unsealed.
This is a basic process. Simple but time consuming. You can skip steps but for adhesion and longevity I would work through them. Hope this helps.