It depends on what you're trying to do: Full power magnum hunting loads, or plinking loads loaded to 44 Special velocities?
Assuming you mean full-power loads, then 2400 is the best choice of the three. But either Hodgdon H110/Winchester 296 or Accurate #9 are better than 2400. (H110 and 296 are the exact same powder in different packages.)
I used to use Blue Dot for my hot 9mm loads, but I stopped after Alliant started issuing warning about its use in .357 and .41 Magnum. If you go to the Alliant site, you'll see they only list Blue Dot loads for .44 Mag for a couple of bullet weights, and in both of those cases 2400 delivers better velocity than Blue Dot.
By the way, I now use Ramshot Silhouette from my 9mm loads, and I'm very happy with it. Muzzle flash is much less than with Blue Dot.
Unique is fine for light loads, although there are plenty of other powders just as good if not better than Unique for this purpose.
All three of the powders you mention are pretty old. Unique came out over a hundred years ago, 2400 dates back to the 1930s and Blue Dot came out 40 years ago. There are newer powders that have better characteristics. For example, Hodgdon Universal is a good substitute for Unique. Power Pistol and Ramshot Silhouette are similar to Blue Dot, and AA#9 is an excellent powder for magnum cartridges.