Why not just prime and paint over the brown? I have stripped paint off many pieces of furniture. It is an onerous task and will be even worse on cabinets that you can't move around or take outside. I love having the inside of my cabs white. It is clean, I can find things easily and my dishes look nice against it. I've had cabs that were dark inside, stained wood and white. I prefer white. What colour are you doing the outside of the cabs?

I wasn't sure how it would look with several layers of paint on it, so that's why we're considering stripping the current paint off.

We are thinking of doing the floor cabinets gray and the ceiling cabinets white. I am thinking of doing the insides white, but if we didn't, would you brush over with a varnish and/or sealant?

If the looks bother you, take the drawers out and spray paint them with white gloss cabinet paint.

Two layers of paint won't make a difference, and it's inside a drawer anyway.

Daisy_chain, join the 21st century.

That said, Citristrip will take off all the layers of paint while you watch TV and eat bon bons. Or something. A 2nd coat will take any stain left out, and you can come down to beautiful, raw wood. No sanding, just sloughing off the goop with a plastic scraper. You probably won't need to scrape at all. I never do. And if you goop it into the corners, it'll bubble the old paint out of any detail on the piece. I always smooth it with a 220, since liquid raises the grain, but it's a smooth, not a grind to a new level of raw.

As far as recoating or painting them, it's what you prefer. If you put away wet dishes, I'd coat raw wood with something. If you paint them, use a latex paint meant for cabinets such as Cabinet Coat.

A finish doesn't have to be shiny. Paint base is a totally matte finish that doesn't need to be fussy. I use it on my stripped cabinets and even doors now, just to seal them and have them look unfinished. I'm fancy that way.