How do I know the best paint technique for white over grey?

I'd just recommend using a very light grey paint. If you take a look at THIS POST I wrote about the paint colors in our former house, a 100 year old house, you'll see the very light grey I chose for the kitchen. That room had no direct windows in it, and the grey color was still very light in there.

I am not quite sure what you mean by best type? Usually in kitchens you use a glossy or semi gloss finish because it is easier to clean. For cabinets, most lines of paint designate one line as better for cabinets. For best results use the best primer you can afford and clean any greasy spots with tsp or another good grease fighter. You can use enamel, but I have had good luck with just regular latex paint.

Sherwin Williams makes a paint color called Crushed Ice. It is a very light gray with just a hint of color in it--toned down--you may like it! It is very soft, not overwhelmingly gray, and a neutral color. I used it in my dining room after my DIL painted her bathroom with the same color. LOVE IT! You can buy a sample and try it!

I'm in love with Fusion Mineral Paint. The coverage is amazing and they have true gray colors. I used the paint on fabric chairs and they came out great. You can read about it and see the colors I chose here https://ourcraftymom.com/how-to-easily-paint-fabric-chairs-with-fusion-mineral-paint/