The origin stories all funnel into a central point, so I guess it's what you want to role play. If you're going for self immersion, again, it's comes down to what you think would be the most enjoyable.
I can't stand tanking in Origins. Plus I enjoy the characters who can tank so I don't mind not tanking. Archery is broken, in the bad way. So don't bother with it. DW Rogue hits really hard, but you have to constantly be in a flanking position for Backstab crits to proc. DW Warrior also hits pretty hard, but no reliable crits makes it less appealing (to me anyway) to play. 2H Warrior isn't great outside of it's abilities and even then, you've got a lot of downtime with slow and clunky auto attacks to fill the void (unless you build a party specifically around it and in which case, it's not even worth it imho). Mage has awful armour and is fragile, but is the most useful class out of all 3 classes (again, my opinion). Mage varies greatly across all 3 games (well, 2 is more similar to Inquisition) so you'd be fine to do that if you wanted. Also, Warden Human Mage and Hawke are related, so that's a cool Easter egg.
If you want a quick play through on Origins, Mage is the only class, which can heal, does the most damage and has the most AoE/Single Target CC out of all the classes so I'd probably recommend that. Otherwise, a Duel Wield Rogue is also a lot of fun and hits really hard (although most of the damage is single target).
As for Origin stories, I'd say all 6 of them are pretty interesting. It depends again on what you find interesting or what type of character you want to roleplay. The mage one is the longest and probably the least exciting, but you learn a lot of things about mage life, which might interest you if you want to play mage in Inquisition. I personally found the Human Noble origin the most satisfying. The City Elf one is also quite interesting, albeit slightly cliche. The dwarf ones are really straight forward and both have excellent writing. I didn't really enjoy the Dalish one; however, it doesn't mean it's not great in it's own way.
In DA:2, every class is extremely viable (they fixed 2H Warrior and Archery) and again, it comes down to your choice. I liked my mage play through, but I canon a DW Rogue in that one because I was determined to canon a Warrior in DA:I, however, I fell in love with my mage character and his romance option way too much.