I was taught by a pro in million dollar ocean front condos and have painted hundreds of cabinets. I've never stripped them. That would be a big waste of time and effort.
Remove the doors.
Clean doors and frames with denatured alcohol or tsp.
Lightly wipe down/wet sand all surfaces with 400 grit.
This is not heavy sanding, just a brief wipe down to prep the surfaces and should take less effort than the cleaning step, but be thorough and wipe all surfaces. You may find an old drip or grease stain that needs attention, or you may find this step completely optional. It does not HAVE to be done.
Dry and dust surfaces until 100% dust free. My old painter buddy liked to blow dry them with compressed air before we would...
Apply a thin coat of primer. I start with the frames and move to the doors. I like working with a bag of cheap foam brushes for this stage. Use dry foam brush to quickly soak up any drips and keep things smooth.
By the time the last door is primed, the frame is ready for finish paint. Thinly applied primer needs 30 minutes to an hour in most conditions. If it is very humid, wait an extra hour and finish the job.
But here's why I wanted to post. The last job I did was my mom's master bathroom. She rents the place and lives with me. I put in a new tile floor, which forced me to do new baseboards, which came with matching crown (thanks mom, god I hate crown), so we decided to paint the door, cabinets and new and old trim all the same
Satin Heirloom White. Yep, cans of spray paint. I don't know what is up with the price in that link, but that can of paint sells at HD for $4 or so. I also used spray cans of Painter's Touch primer for the cabinets and entry door; the new base and crown came primered. In all I purchased 12 cans of spray paint for less than $50. 4 cans of primer and 8 cans of finish. I sprayed the base, crown, and doors outside. When I punched finish nails into the base and crown while installing, I just needed a dab of filler in the nail hole and a quick squirt from the can to get a professional look. It was so much easier to spray outside that this little finish step inside was way worth it.
The point is for smaller and maybe even medium sized diy paint jobs, spray cans may be the better choice. No brushes means no brush marks, no brush clean up, no paint stirring, spilling, dripping, storing etc. Just shake like a monkey and spray (actually a little technique is important, but still). The high price of paint by the gallon is what got me thinking of cans. I would pay a premium to use cans next time, but for this job it seemed to break even or save a few bucks. More importantly the paint in those cans is oil based, so I got a richer more durable finish than I would have with water based brushing and messing with cans. When I was doing the bathroom door outside, I was getting a very fine pimpling from the cans. It was like a tiny paint rash you couldn't see but could feel with your hand when it dried. This was from the very fine spray drying almost on contact in tiny little spots. I needed to keep the can closer to the surface than I would with a paint gun. Once I got the distance right the job was a snap, a very clean, very disposable, very professional, in and out snap.