Human
Noble or Wealthy: Probably some sort of military position, captain in the army or something... if not, then some sort of political job or a merchant.
Peasant: Blacksmith would be my number one choice, next would be a tailor, or a cook for a tavern or a noble house.... last would probably be a farmer, too out in the open and prone to being burned down by darkspawn, bandits, loghain, and rogue mages and templars.
Elf
Dalish: By far number one choice, city elves lives suck... would have to be a hunter, or a craftsman
City Elf: Welp, would rather die than be a city elf, but if i had to.... i would at least try to apprentice myself to some sort of craftsman, opportunities being very limited for elves. Like hell i will be a noble's servant, im not one for getting whipped.
Dwarf
Has a caste: Warrior caste is the first choice, but fighting darkspawn is inevitably fatal... smith caste next, i like making stuff, what can i say?
Casteless: Yeah, im heading for the surface
Surface: This is where i get kinda weird, as a dwarf i know i can drink, so i would earn all my money by wandering to different taverns and challenging people to out drink me.... easy money.
Qunari
Qun: Welp, whatever they decide im there for
Vashoth: Merc, definitely a merc
Bonus
Dragon: Gonna chill up on my mountain and eat stuff, until a random group of people decide to try and kill me.... im just there to be loot