Question about [ I ] and [ me ]

I know, that I should use [ I ] as a subject, and [ me ] an an object. But I am a little bit confused about this:

- I like coffee.
- Me too. (is it an exception, or I should use [ I too ], because [I like coffee too]?)

+ smth. strange here. I had written in my essay smth like [I and Susan went to Thailand last year], and someone corrected me, that it should be [me and Susan... ], but I haven't found this word order in rules to check it. Every example I found has an order such [Susan and I ...]. Do native speakers tell [smb and I] every time, or [I and smb] correct too?... or in this case it should be [me and smb]?