Well, I like oil based primer and enamel. The biggest problems with oil based products is they small bad and take a while to cure. With children in the house the smell is a major concern. Acrylic primer and paint will work very well for you and dry much faster without the harmful VOC's.
Choose very good quality products for your cabinets. And apply multiple thin coats instead one thick one, example- 2 thin coats of primer and 2-3 of the paint. For good washable surface choose either a satin or semi-gloss paint. the semi-gloss is a better choice all around.