I have created some new content types but they automatically don't show up in the 'Create content' menu - what do I have to do to get them there. I am currently logged in as user 1 so it shouldn't be a permissions issue.
I think you are facing the same problem I've experienced. Probably you disabled the navigation menu link "Add Content" and its respective sub-menu items. Then, they won't show up at the path node/add.
See this Q/A: No content type problem