1- Had better: We use had better to say what is the best thing to do in a particular situation. 'You're ill. You had better see a doctor, NOT You have better see a doctor.' 'I'd better tidy this room up.' 'Had better' is stronger than 'should' or 'ought to ', although it is not as strong as 'must'. I'd better tidy up means that I am going to tidy up, because it is the best thing to do. The negative is 'had better not.' 'Come on. We'd better not waste any time.' 2- Would rather (NOT had rather): Would rather means 'prefer' or 'would prefer' (we use it to express preference) 'I'd rather walk than hang around for a bus.' 'Would you rather eat now or later?' The negative is 'would rather not.' 'I'd rather not take any risks.'

Had better... Would rather.... No such phrase as "had rather"