Currently on my first character (male elf mage) and planning to spec him either as a Rift Mage or Necromancer. Rift Mage suits a Dalish considering the use of Stonefist while Necromancer is more of a focus on the Entropy tree.
As far as other race/class combos, I'd say:
Human- Definitely warrior or mage. For non-mages, a noble groomed in the service of the Chantry would best fit around a warrior, either as Champion or Templar. Even if he/she is not religious, I can see him/her being trained in that field or expressing an interest due to familiarity. For mages, a Knight Enchanter is the best bet since the fighting style is very 'Circle Mage-y'. Necromancer second for non-lawful/more darker characters.
I can't see a rogue for humans due to his/her background personally, but I suppose an assassin fits (trained in archery/espionage).
Elf- Rogue or mage. They're relatively very skinny, so I can't see an elf in bulky armor wading on the front lines or wielding a gigantic sword without anime/jrpg comparisons. For a rogue, I'd say go the archer route (elves and archery, stereotypical I know) and the assassin tree best suits a Dalish hunter. A tempest 'could' work as well, a Dalish who spent his/her time experimenting with various concoctions and testing them on their prey.
For a mage, as I said before, a Rift Mage suits a Dalish best (Stonefist) though Necromancer isn't too unusual.
Dwarf- Normally I'd say warrior, but a rogue suits a dwarf better due to his/her association with the Carta (and being sent as a spy to the Conclave). Pretty much any weapon style and specialization works here. Assassins are for the cutthroat, get the job done in the best and most efficient way possible types. Artificer for the clever ones who like to spring traps (and dwarves are mechanical). Tempest for the crazies who like to douse themselves and wade into battle.
For a warrior Cadash, a more heroic dwarf might do well as a Champion or Templar, possibly one who had a past but turned a new leaf and took up a new way. Templar for pro-Chantry dwarves (as a surfacer, its possible Cadash believes in the Maker) while a Champion is more neutral. Reaver could work for a thuggish dwarf, best to go with a two hand style for maximum damage.
*Ironically, dwarves are the most versatile in terms of class/weapon/specialization choices as opposed to others, even human.
Qunari- Due to their size, I really don't see Qunari as rogues, though it wouldn't be lore breaking if they were. Personally I'd prefer warrior (they are big, tall and strong after all) then mage.
For warriors, a Champion for a more defensive qunari and a Reaver for a more chaotic one. Templar doesn't suit a Qunari well unless you rp them as a converted Tal-Vashoth. Still, they just don't seem very Chantry-like.
For mages, I would go with a Necromancer since a Tal-Vashoth would probably gain more by intimidating and manipulating his/her foes. A knight enchanter could work given the qunari's size and general likelihood of wading in the front lines no matter what. Rift mage with the focus on the AoE rings can also work.
Pretty much any specialization works with rogues given the qunari is a Tal-Vashoth mercenary and thus more versatile (not nobility or having a strong predefined culture). A more clever, tactical qunari would be placing traps as an Artificer. The qunari do use toxins, flasks and concoctions a lot, so Tempest isn't unusual. An assassin works with agent-style Qunari.
(Just my thoughts)