My question now would be, how much German does my partner need to speak? Grundstufe? Mittelstufe? I'll appreciate any answer, but the one I'd appreciate the best is a pointer towards where to get the official documentation, so that I can check things on my own
If you are not married, your partner has to apply for a residence permit independently, and therefore fulfill one of the criteria under which Germany allows residence (e.g. work, or bringing 0.5 million euro in to the country). If you are married, it is a different story; as you are a non-German EU national, your partner would qualify for a residence permit under Section 30 of the Aufenthaltsgezetz. (English: http://www.en.bmi.bund.de/Internet/Content/Common/Anlagen/Gesetze/Gesetze__Sprachen/AufenthG__en,templateId=raw,property=publicationFile.pdf/AufenthG_en.pdf German:http://www.gesetze-im-internet.de/aufenthg_2004/index.html ) which requires that "the spouse is able to communicate in the German language on a basic level at least". If you got married, came to Germany, and your spouse applied for residence after arrival, he or she would only need to satisfy the interviewing immigration person that their language skills were adequate. If he or she applied for the residence permit from the German consulate in the USA, its more formal and he or she would have to pass the A1 language exam.
As always, I'm not an immigration officer, so best to double-check any advice with the German consulate in the USA.
Good luck!