If you are just painting it, you don't need to expose bare wood. <Staining is different, in that case you should use a chemical stripper - they make water based one that is not too bad.>
All you need to do is to scrape off all the loose finish, sand to scuff up the surface & feather off any eneven paint areas. After that I'd use a solvent based primer <that cabinet looked lacquered & regular paint won't stick to that!>. Try to find a primer specifically for old paint if you can (avoid water based primer as that will not stick to lacquer). After 1 or 2 coats of primer, you can top coat with the paint of your choice & seal with urethane.
80 gal FW with 30 gal DIY wet/dry/sump.
9 fancy golds, 1 hillstream loaches, 1 rubber-lip pleco (C. thomasi), 3 SAEs, small school of white cloud minnows, planted.