Hi,
You're right - me too is more informal.
So do I, so have I, so am I etc are more formal.
To choose the verb, imagine the statement as a Yes/No question, and use the verb from the question. For example:
I'm really tired => Are you really tired? (are is from the verb be, so the response is "So am I")
I've been busy recently => Have you been busy recently? (So have I)
Hope this helps
Kathryn