I don't know if you've been to Europe before, but if you haven't, I would suggest you pay close attention to lancebanyon's advice and not try to drive as soon as you get off a transatlantic flight.

Also, I would reconsider driving and think about taking the train. As you note, most discussions focus on dissuading people from driving and taking the train instead, and there is a very good reason for that. Trains in Europe are nothing like trains in the US.

But regarding the drive, I would go for the direct route. I can't think of any particular reason to go through Luxembourg. Note that the drive will take you longer than an equivalent distance on a US interstate.