We use should to talk about what we think is a good idea for someone to do i.e. to give advice.

Ought to and should have a very similar meaning. Should is more common than ought to, which is more formal.

We use had better to talk about actions we think people should do or which are desirable in a specific situation. Had better is a bit stronger than should because we use it when we think there will be negative consequences if that person doesn’t do what we’re suggesting.