Depending on the number of people involved in the company and the amount of capital you have, different legal structures could be advisable for your business.
In principle, partnerships ("Personengesellschaft") and corporations ("Kapitalgesellschaft") are two distinct business forms you can choose from: In partnerships, the shareholders are liable for their private assets. The companies based on such partnership include businesses with GbR, KG, GmbH & Co. KG, PartG, PartGmbB and OHG. For example, if you run a small trade ("Kleinegewerbe") with a partner, you are automatically considered to be a Company Constituted under Civil Law ("Gesellschaft bürgerlichen Rechts" or GbR). For such business, no contract and no minimum capital is required. When you register for a trade or a freelance profession, you automatically set up a sole proprietorship and are responsible for your private assets - even if you don't establish a company.
If you build up a capital company, only in exceptional cases you would be liable with your private assets. To this end, corporations must disclose their annual financial statements publicly. Capital companies include the ones with GmbH, UG and AG abbreviation in their title. As a sole founder, for example, you can build an entrepreneurial business ("Unternehmergesellschaft" or UG). To do so, you only need a one Euro starter cash and would not be personally liable for private assets.
Cooperatives ("Genossenschaft") is a different business form. It also excludes liability for private assets but is categorised neither as a corporation, nor a partnership.
The suitable legal structure for your business depends, more than anything, on the number of shareholders and their professions, the size of the proposed company and the available capital. Before making the decision, you should consult a tax advisor or a lawyer. You would be able to change the legal structure, even after the foundation.