The registration to the city's office ("Anmeldung") should be the first thing to do. It's not necessary to have a rent contract to do so, the communication of your current domicile and a valid proof of it ("proof" can in some cases even be your Hotel's receipt, or a letter signed by somebody who is already registered in the city stating you are their guest).
The next step would be the bank account. Most banks, including Berliner Sparkasse, only need the registration document to open an account.
With the registration + bank account document you can request a Schufa, which is the credit documentation that will allow you to apply to apartment rentals. I strongly reccomend though, until you find a job, to try to find temporary accomodation (many offer 2, 3 months-rental of furnished rooms) because at least three months of payslips is a common requirement while applying for an apartment.