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.'