Furniture, Wood and Cabinetry Finishing - Refinishing veneer bedroom suit

I have a 5 peice bedroom suit that I would like to refinish. I believe that most of the body of the furniture is wood, but the finish of it is a very dark brown, I guess you would say it's veneer. It is flaking badly in areas sorta like onion skin?? There are also a few spots where the finish is bubbled under the surface and is cracking. If you rub it, it chips off and you can see the wood underneath. I would like to paint the entire suit a lighter color, not stain. Is there some type of primer or something I should put on first so the paint sticks, or do I need to strip it first?? Thanks for your input.

Sand thoroughly, removing all surface irregularities. Prime with BIN or KILZ (2 coats) sanding lightly after each coat has dried. Paint with your choice.