Carolyn: any GOOD latex paint will do the trick. Make sure to prime on a clean surface too. Do not skimp on quality. Then treat the cabinets gently for a month or so --- to let the paint cure.
I would use latex enamel.
Now I only use Fusion Mineral Paint for cupboards - it's so durable and the colors are gorgeous! Here: https://amzn.to/2DTHILi
Here's a post that might help - https://homeguides.sfgate.com/refinishing-mdf-cabinet-doors-34268.html
so a gel paint willnot work?
Take a cabinet door front to the paint department and ask for their advice on materials and application tools.
depends on whether they are Kitchen /Bathroom or elsewhere. If Kitchen/Bathroom only use Satin or Eggshell finish or Gloss. Elsewhere, you can use any paint including Emulsion, Chalk paints, but do seal with, either Wax or Polyurethane....................
This is the only paint I'll use for cabinets: https://bachelorettepadflip.com/2018/04/09/why-i-had-my-kitchen-cabinets-painted-twice-in-two-weeks/
First, a good coat of primer (not primer+paint). I use Kilz. Then you will need at least two coats of latex enamel gloss paint. This is a harder paint and will yield a more durable result than semi-gloss. Also, I recommend applying with either an HVLP or a very fine nap roller.