Ægteskabudengrænser.dk

I'm an USA citizen, and I'll move to Denmark on Tuesday. My Danish fiance and I will be getting married on the 21st of January, so I'm trying to double-check and make sure I've got everything ready before I go. We're planning to use the Sweden method to get me residency in Denmark.
I have my birth cirtificate, my social security card, my passport, and an official paper saying that I am single. Is there anything else I need to bring with me or make sure I have on hand to get married in Denmark before we move to Sweden?
Does anyone know if I need to do anything with the US government before I leave the country? For example, let the government know I am moving out of the country? I don't have much experience with moving internationally, so I have absoutely no idea.
Any help at all will be appreciated! I'm sorry if I'm asking things that have already been answered on the forum, if there are other threads regarding my questions, please direct me to the thread that will help me! Thanks a bunch.

Yes, you do need to inform the American authorities, that you are going to move abroad. Also make sure to drop the same information to the post office there and to any place where you subscripe anything.

But perhaps no need to do so, until you actually are settled in another country and have a personal registretion number in that country. Until that time you are actually only on a sort of extended vacation, which you hardly need to inform the authorities in your own country about.

Ok, that was helpful, thank you both a bunch! You guys and this website are awesome. Thanks and merry Christmas!