I know this isn't what you asked... but if I were a Daedric Prince, then I would be in addition to the existing Princes... since they would already exist before I did.
As such, I would be Thervyn Ryf, Daedric Prince of the Lost, Forgotten and Unfound. He would occupy a role that is in some ways similar to Hermaeus Mora and Malacath, and yet still quite different than either of their spheres of influence.
Were I restricted to an existing Prince, I think I would actually go with Hermaeus Mora... as he basically knows everything there is to know. However, my first order of business would be to change my voice and stop appearing as nasty ooze and tentacles.
Definitely Hermaeus Mora or Malacath. These 2 are complete opposites but I can easily act both of these personalities. In real life I'm a pretty smart person, and I'm also aware of most hings that go on around me, not many secrets are kept away from me. But I also take many fighting classes and i'm kinda arrogant so I guess I can be either of these.
Sheogorath is fun and probably the sanest god I have ever come across but I think my first choice would be Malacath whose sphere is the patronage of the spurned and ostracized, the keeper of the Sworn Oath, and the Bloody Curse. He is protective of his followers and will wreak vengeance on those who harm them. The Orcs are special to him and the follow the Code of Malacath.
As a rogue my second choice would be Nocturnal.
The Daedra Princes are neither male or female but choose which aspect they will use to show themselves to mortals.