Well, let's see.....I've got a few ideas. They can be either gender, really. Straight or bi if at all possible, but that would just be my personal preference, and have little to do with their actual character concept.
An exiled dwarf of Kal-Sharok or Orzammar. Put in some drama about WHY they were exiled, who they were before then, and how life on the surface has changed them and what they've been forced to do to survive since then. Might be cool for them to debate the validity of dwarven religion versus the Chant. And give them a healthy disrespect for the Carta.
Someone from the Anderfels, probably a ranger or scout, but not a Grey Warden. Fairly devoted the Chantry(As most from the Anderfels are) but also fairly neutral as far as politics are concerned. For flavor, I'd give him/her a theme of survivor's guilt. Maybe a village lost to the Darkspawn(or whoever the Enemy of DA4 is, making them plot-relevant), giving him/her a sense of duty towards those who are helpless.
The third/fourth/fifth/etc child of a noble out to make a name for themselves. Talented and ambitious, they want to have more than a life of comfort and stability, they want to EARN the right to be called noble. Rather than be married off or take a job that offers them a steady income for the rest of their lives, they make the decision to go out into the world and do something with their life. But they are too individualistic for the military, Grey Wardens or the Chantry. But they still love their family and their life from before. They just have a large chip on their shoulder over how easy they've had it compared to others.
Lastly a mage who is unconcerned with the great mysteries of the world or changing the current social order. They're not on some damned-fool idealistic crusade(Merril, Anders or Dorian), nor are they mysterious and deliberately obtuse to hide their true, secret agenda(Morrigan, Solas and Vivienne). Just a man or woman who is concerned with doing the right thing and using their gift to make lives better. Maybe a person who just wants a simple life and a family, but his/her talent and circumstances have prevented that possibility, until they meet the PC. Maybe a backstory that involves one very big mistake that resulted in a lot of pain, one he/she regrets terribly and does their best to make up for.
Those are my ideas, anyway.