There are some differences between traders and freelancers regarding the suitable legal structure. The choice is limited for the freelancers, though there are some special legal forms, especially with regard to the liability limitation. Freelancers do not register at the Trade Office but directly apply for a tax number at the Tax Office (Finanzamt).
First of all you should check in advance with the Chamber of Industry and Commerce or the Chamber of Skilled Crafts to find out what you need in order to register your business. You can also use the services offered by the municipal authorities and regional business development units. Also the municipal authorities can tell you if you need any special certificates, permits or preconditions.
A person who starts a company and who is not a freelancer is a trader. Traders have to register their business at the Trade Office (Gewerbeamt) in the municipality where they are going to start their business.
Business people and companies like the Limited Liability Company (GmbH) have also to be registered in the electronically Commercial Register (Handelsregister). Usually you do that with a notary (Notar).
If your business is part of the craft sector that needs a licence you will have to ask for an exception for your registration in the Trade Register (Gewerbeamt) at the Chamber of Skilled Crafts (Handwerkskammer).