I thought about what I would like for a bit longer, so here are some things that interest me:
- A system that encourages the development of strong stories, in which the characters and their motivations and convictions actually matter mechanically (Im rather fond of how you can tag someone's aspect in Fate)
FATE, yes, as well as Burning Wheel, Pendragon and Reign spring to mind. But most of all, if you want to go 'hard left', so to speak, and
really ditch D&D for a while, HeroQuest might seem the obvious answer. In that game, a PC's qualities as written (distilled into 'Keywords')
are his or her game mechanics. Burning Wheel and Reign both feature lifepath systems, if that means anything - for good or ill - to you.
- Dice Pool etc welcome but not a must
Reign features a rather unusual dice pool mechanic. Quite clever and neat - height
and breadth of numbers are what matter. That is, each is considered discretely.
- Doesn't have to have an inherent Campaign setting as I may want to use my own
You'll have a hard time finding many RPGs that don't have at least some kind of
implied setting. HeroQuest (2.0) might be the closest thing here, though any of the above (particularly the fourth edition of Pendragon, in that instance) wouldn't suffer overly much for the removal of what setting material might be contained, suggested or implied.
You could, of course, import aspects (haha) of one system into another. Traits, Passions and Glory from Pendragon, Aspects from FATE, Keywords from HeroQuest, Beliefs and Instincts from Burning Wheel, or whatever else you like the sound of - adjust stat references and maths if necessary, and done. I bothered mentioning this because, well, I've tried it and it worked for us. Perhaps it could for your group.