I love the idea of being a dwarf of the Ambassadoria, or one of the many underground embassies in Tevinter. It's a nice mesh of traditional dwarven culture and the surfacer stereotype of dwarves as greedy lyrium smugglers/merchants - just the glorified version in Tevinter, for obvious reasons.
My biggest concern would be the Qunari invasion, because I feel like that immediately puts us at odds with the Qunari and I'm much more interested in a grey versus grey scenario. Half the point of Par Vollen and Tevinter is that they're both pretty horrible (and also awe-inspiring), and I wouldn't want new players automatically sympathizing with Tevinter because that's where they started. It's not as interesting to me.
In some ways, I'd rather start on Seheron. Now THAT is a perspective I'd love to explore.
Yeah the problem I'm seeing with all four races is that there's no easy method of having them end up in the same starting place. Obviously Bio will probably pull a Warden or Inquisitor where the PC becomes some figure that transcends race. But the social disparities available from the races to begin with will make this a challenge.
If we are not playing a Qun following kossith, which seems the most likely option, chances are a kossith PC would have to start as a slave or else a Tal Vashoth mercenary. I think a dwarf would realistically have to be an ambassadoria dwarf. From all that we know of Tevinter, the majority if not all dwarves in the country are from the ambassadoria, and are highly respected and their own social class. We could learn that there are surface dwarves living there, but AFAIK that has not been made clear. We know there are no Dalish in Tevinter, for example, so I think a lot of the social norms we've grown accustomed to in the South won't be in the next game.
Elves and humans have a wider range of background options. And if Fenris' sister can be apprenticed to a magister (assuming Danarius wasn't lying to her), then it seems elves can be just as powerful as humans. I would think there are far fewer elven magisters, though, and they might be second-class citizens of the magisterium. Presumably they would not be descended from dreamers, so they wouldn't have the distinction of heriditary blood lines as much as the human Tevinters do.