"Should" and "ought to" are both used when giving advice and to say that something is the best thing or the right thing to do (there is no difference in meaning), but "should" is much more common. You should give up smoking. "Had better" can also be used to say what is the best thing to do in a situation that is happening now: We'd better hurry or we'll miss the train. We could use "should" or "ought to" in this example, although "had better" is stronger. The speaker sees the action as necessary and expects that it will happen. Also, with "had better", there is always a danger or a problem if you don't follow the advice. "Should" only means 'it is a good thing to do': It's a great film. You should go and see it. (but no problem if you don't) The film starts at 8.30. You'd better go now or you'll be late. You form the past by using "should have + past participle" or "ought to have + past participle": You ought to have been more careful. She should have seen the doctor.

Using "had better" often implies negative consequences if an action is not taken or completed. It is advice, "We had better not miss the show, OR [you will be in trouble]." Using "should" is more the opinion of the speaker, "We should not miss the show, BECAUSE [we arrived 30 minutes early]." In some cases they can be used intechangeably, as in your 2nd example. Generally however, "had better" indicates a stronger level of feeling from the speaker.