Just want to note that if you're not tied to Germany in particular, Netherlands is a much better option for US citizens looking to start a company, thanks to the Dutch-American Friendship Treaty. (yes, it's DAFT - https://en.wikipedia.org/wiki/DAFT). NL is a pretty easy place to business, at least as an entrepreneur. (Things get more complicated with lots of employees, like in most of Europe.)
The tl;dr version is US citizens can get a residency permit (2 years, renewable indefinitely, considered a non-temporary purpose of stay so you're eligible for permanent residency after 5 years) to start a business in the Netherlands with very few restrictions and very little in the way of capital requirements (€4500 in the business account.) Plenty of attorneys in the Netherlands can take care of the necessary paperwork for €1500, give or take, but lots of people manage it themselves too.
A few blogs and guides of the many out there:
https://daftvisa.wordpress.com/step-by-step-guide/ https://survivingdaft.tumblr.com/ http://passthesourcream.com/daft/