To do list when moving to Germany (Frankfurt)

Hello everybody,

I need your help to build a to do list of things I need to do to start my life in Germany...

So, in two weeks I will move into the flat I found (with a big effort) in Frankfurt.
My landlord should give me the "final" contract as I'm moving in. With this, the first thing I will do is register my address (Anmeldung).
Next thing I would like to do is to start my public health insurance (still have to decide what but I read they all are quite similar). As far as I understood, I need my registration and my employment contract (open end time)... Then will I be ok?
Last, since I already have a German bank account, I will move it from Friedriichshafen (when it is now) to FFM. I already asked in Deutsche bank and I just need my registration and my passport.

Considering that last year I spent 7 months working as trainee in Germany, what else shoul I do to consider myself ok? Like taxes card etc.?

Thanks a lot,

Elia