If you're researching a Minnesota family, the Minnesota Historical Society should be on your to-visit list. Their collection is incredible, both online and in person. While I haven't yet been able to visit the MHS in person, I've found it helpful my family research. Online catalogs of their museum collections have helped me identify family artifacts. I've also used their naturalization indexes to determine that a family member had in fact been naturalized, despite his behavior to the contrary.
This morning, I discovered another resource that I look forward to using. The MHS offers a Family History Resource website. That site contains lists of local genealogy societies and suggestions for how to research different kinds of records. The level of detail is fantastic, especially if you're not used to doing research in Minnesota. Unfortunately, the Luxembourg links do not appear to be live, but I'm sure you can find more resources under "German."