How does German trade tax/ corporate tax work?

Hi, we are a UK startup thinking of relocating to Germany. We are still a small team and have been collaborating with German partners for a while.

We are wondering if we should incorporate in Germany as well once we are based there. Brexit has caused some serious uncertainty about having your corporation registered in the UK but your HQ on the continent. However, we are a bit unclear about the tax burden our startup would be subject to in Germany. I understand there is a corporate tax and a trade tax, and the tax rate is determined by not just the (federal?) tax code but also by the municipality or state your are registering in. How does this work exactly and where is the "best" place to register within Germany (lowest tax rate)?