If it were me, I'd pick either DUS, CGN or FRA as my arrival airports and take a train to Minden from there upon arrival. You can easily check rail connections on Bahn.de and see what makes the most sense. Minden has direct InterCity-Express connections to DUS airport and can be reached in about 2 hours. From FRA is 2x that travel time and all services have at least 1 connection. I don't mind the connections when traveling alone, but with luggage and for anyone who isn't familiar with German rail, it can be a real stressful experience to try to get off one train and onto another within 3-4 minutes.

On the return, I suggest you take an evening train the night before from Minden to either Düsseldorf or Frankfurt city center and just get a hotel there for the next morning's flight back to the USA. Avoid the stress of an early-morning wakeup and hoping the train's running on time, etc.