I am buying a '40's house with HORRIBLE tile on the bathroom walls, how to paint over them?

I LOVE THIS HOUSE. It has a swimming pool, and everything, but the only bathroom is small, and the walls are covered in BLUE tile!! Not one of my colors, nor a color I like. It looks like they have recently put down linoleum on the floor, so I can replace that. What I’m concerned about is the tile. Should I try to remove it, or paint over it? And if I do paint over it, will it stay? Keep in mind that the tiles are not only on the walls, but the entire bathtub walls are covered in them. I cannot live with this, and want to change it. I’ve never done any DIY, other than painting, but between this bathroom, and pulling up the carpet to refinish the hardwood, I’m going to have to learn!! Thanks in advance for your help.
No, the tile is not plastic, it’s ceramic.