Paints and primers will fill in somewhat as the layers build, but the grain will still be visible, more so if you use a shiny paint, like semi-gloss. Some mind this, some don't and figure it's okay if their painted wood looks like wood. I don't have personal experience with grain filler, but Faron has raved on here about FPE (Fine Paints of Europe) Brushing Putty.

Thank you for getting back to me.. I will look into that.. is that something you purchase at a store, home depot? or order online?????
I am in the USA... are they in the USA..

huggles

FPE Brushing Putty
Fine Paints of Europe Retailers

A heavier bodied primer like Benjamin Moore Fresh Start Alkyd Enamel Underbody might be worth consideration, too. It's designed to level well, creating a smooth surface for top-coating with paint, and an oil based primer won't raise the grain the way a latex based primer could.

Here is a link that might be useful: Many recommendations on a Kitchen Forum discussion about painting cabinets