Hi Gale, acrylic paint and primer will do just fine on your cabinets. Make sure and clean them really well first before priming. When my mom and I painted out her kitchen we did two coats of primer, three coats of paint and then two coats of a clear semi gloss polycrylic and they're holding up so far really well!
Great information here about primer and paint along with prepainting suggestions:
Gale: I have had YEARS of good luck just using a good primer and then a good brand of of latex paint (2 coats - maybe semi gloss for tougher finish.). ...don't buy the cheapest thing out there. ...ask the paint professional at the store for the best quality paint to use.
Here is an article that might help on choosing the best paint.
As for primer, I would go with Original Kilz to make sure you have no bleed through.
Make sure to number all doors and drawers and keep all hardware in a sealed container. It's the worst when you are trying to put everything back and they have gotten mis-matched or you are missing something.
I am a strong believer in oil based paint. It is most durable and stands up to cleaning and moisture. It looks prof and brush strokes are minimal. It's all I use on all wood.
Oil based paint is great but smells terrible and is horrible to clean up after. I lightly sanded my cabinets and then applied a good bonding primer/color blocker. I have done my cabinets 2 ways by brush and roller. Use a mohair roller and with a sprayer. I must say I like the sprayer much better because no brush marks. But more difficult and more work.
I like the smell of oil and clean up is a breeze if you do it right. Only have to clean up once after totally done. Brush and rollers stay good once wrapped in handiwrap and put in freezer during job. Or you could just throw away when done.
I've had to fix too many paint jods where someone used latex over oil or varnish and it peeled. So I do a lot of prep and use oil. Never had a issue. To each their own.
Gale....I used Kilz, Behr and Zinsser and find all good primers. You can find primers that have paint in them. This will save a few steps if you use them.
This is what I used, I am happy with the results! https://thehoneycombhome.com/painting-kitchen-cabinets/
This is the only paint I'll use and here's why: https://bachelorettepadflip.com/2018/04/09/why-i-had-my-kitchen-cabinets-painted-twice-in-two-weeks/