A Great Dane because they make a great statement but are gentle & loving with low energy which are great for a busy lifestyle. Therefore the time spent with them doesn't have to be about play.
If the allergies are mild, the girls will be fine with a Dane. I have allergies & have been fine with our 2 dogs & cat. I detest resorting meds unless washing my hands & face doesn't bring it under control.
Also it should NOT be one of the standard AKC recognized show colors. This makes as much a statement as the dog itself.
Take the Blue Merle (Grey with Black spots) for example: You get some Merles when trying to breed for a Harlequin (White with Black spots) A few decades ago they were drowned as being undesirable. Now the AKC recognizes them as Harlequin breeding stock but still can't be in shows.