Finally making the move - first stop? (Berlin)

Greetings!
I've been holding off on things because we had not yet moved to Berlin - but the movers are booked, the apartment is ready, and we will be there on the 26th of April.

There are a ton of questions (and before you send me to Toytown, I've tried to get approved there, but nobody is answering to the emails for approving my account) and a lot of excitement - I'll finally be ready to get involved with InterNations events!

A little bit of the questions:
Most of our confusion comes from us both being EU citizens (I hold dual USA-Sweden), freelancers (husband is an artist, we're both translators), and while we get started in Germany, we'll still be working for Swedish clients.
I've been able to start a few things. I have an appointment at the nearest Bürger (?) office shortly after arrival so we can get registered as living in Berlin. Husband already has a bank account - he was temporarily in Berlin last year. Schufa won't be needed right away, we are moving in with friends, but there is still the insurance requirement even though we come from the EU. And we have a local person who is willing to be a temporary interpreter for us while we sort through the first few weeks of governmental paperwork. But she won't be available forever.
Eventually, we need to be listed in Berlin as either self-employed, or under a business corporation and husband is working on another venture for retail and so we'll need an accountant too. Plus help with all the fun that entails.

Anyway, that's the intro, for whatever it's worth.

First actual question:
Is it indeed my first stop to go to the Bürger office and get a form filled out that we have moved to Berlin?
Let's start there. Because if that's the wrong thing, I need to rework my scheduling.

Thanks in advance!