I have to with Badger here, strip it down first, because you never know how nice the wood is until you strip it. Good wood furniture is almost always going to look better stripped and stained than if you paint it. If it’s junk, it will still look better painted after you strip off the old stuff.
If you do strip it and then decided to paint it, use the primer first, because you want to seal the wood to waterproof it and keep it from absorbing the solvents in the paint. If you decide to just paint over the old paint, you shouldn’t need primer.
thanks, i am pretty sure based on how soft this wood is that it is pine and nothing really nice that should be stained. Also, this is for a baby’s room and the rest of the furniture is white, so that’s what my daughter is looking for. i do like the darker grey contrast on the shelves and interior of the bookcase, it has no back.