Priming Walls Saves
A while ago a friend of mine phoned in complete frustration. After painting a wall four times, he could still see an old stain. He explained how after the first two coats it looked good, then a few days later the stain was visible. And after his fourth coat and a gallon of paint he didn't know what to do.
My response. "Did you prime the walls?". Of course his response was no. I went on to explain to him that especially with stains, you need to use a sealing primer to stop a stain from coming through your new paint.
Paint provides durability and color, but not bonding and stain blocking.
Save yourself time, frustration, and money. Prime before you paint.