Rather than

Rather than means instead of something or in preference to.

Rather than 意为着代替或偏爱某物。

Rather than complicating matters further, we should just let Martha deal with it herself.

我们应该让玛莎自己处理这事，而不是使事情更复杂。

Would rather / had rather

they are both the same in meaning – when you prefer to have or do one thing more than another. Although, 'had rather' is more archaic and not as commonly used as 'would rather'. Generally, this is used as a contraction (I'd rather) so it isn't always clear which one is being used，but thankfully, they have the same meaning!

它们的意义相同——即当你喜欢拥有或做一件事而不是另一件事。但是“had better”更古老，不如“would rather”常用。一般来说，常用于缩写形式（I'd rather），所以常常并不能确定是哪个词组..但幸运的是，它们含义相同！

“Would you like to go to Sarah's house for dinner tonight?”

“你今晚想去莎拉家吃饭吗？”

“I'd rather stay at home” (I would rather stay at home / I had rather stay at home)

“我宁愿呆在家里”（意义相同，但是形式不同）

Had better

Had better is used to give advice or tell people what to do. The meaning is present or future, not past. Always use had, not have. After had better, we use the infinitive without 'to'. Had better has the same meaning as 'should'.

Had better在给人建议或告诉别人该做什么时使用。意为现在或将来，而不是过去。一般使用had，而不是have。had better之后，使用不带to不定式。Had better和“should”意思相同。

We had better leave early if we don't want to get stuck in traffic. (we should leave early if we don't want to get stuck in traffic – advice/suggestion)

如果不想堵车的话，我们最好早点走。（如果不想堵车的话，我们应该早点出发）。