All else being equal, I usually opt for SAS, Lufthansa, or similar just because traveling on the foreign airline adds a tiny bit more foreign country experience. Food is different and interesting, FAs have those wonderful accents, etc.
OTOT, I usually avoid traveling on foreign airlines where I'm unsure their maintenance standards and crew training are at least equal to that of the US.
You probably need to tell a little more about your desires in a hotel - budget, star level, location, etc. before anyone will jump in with recommendations. I think people that bid on Priceline usually end up with a Marriott in Copenhagen. That could be one route to go.
Romelle