Have you considered starting with something like Once Upon a Time? Although it doesn't fulfill all your requirements (i.e. no character advancement/strategy), it is my impression that it fulfills the main ones: which is heavy focus on story-telling and assuming author stance.
It is an astonishingly fun cooperative game: basically, players get cards representing story elements (such as characters, events or places) and have to narrate a story based on them; the way the story-telling turns flow is very intuitive and quite fun.
In theory, being a card game, it is slightly competitive: i.e. it has the end-goal of winning (which most RPG don't have). On the other hand, in my experience, given the right group of people, the game doesn't necessarily have to follow this flow, and could be slightly adapted to fulfill your needs.
Again in my experience, this game would be a suitable bridge between playing board games intermingled with some story-telling and acting, and going RPG. It has allowed me to introduce people resistant to RPGs to what I feel is the core and most important aspect of them: story-telling and sharing.
It helps the shy because you don't have to intervene if you don't feel like, and can participate just by listening: this is a huge deal for some people, who don't want to feel the pressure of acting in role-play (or even of being asked what their characters do). On the other hand, you will see that, taken this pressure away, most people actually get into the flow and collaborate to the story.
Also, by having cards with elements, it helps both those who have some kind of performance anxiety (people who think they lack imagination) and also makes sure that the story follows some kind of coherent track.
Last, but not least, games are also self-completing and manageable in time: though for me the fact that an RPG campaign can last for years is an astounding thing, a lot of people are intimidated by this statement or don't want to commit. By ensuring that the story closes, you take this away again, contributing to a more relaxed environment.
Depending on the mood, you can get completely nonsense hilarious adventures, or deep and meaningful stories; no matter what, in my experience, people will keep talking about the story and the characters for a while, and it's not uncommon for player to want to start the next game a few days or weeks later more or less where the last one left off (or calling in aspects of that).
And I guess you see where I'm going with this: as players get more fond of the characters, of the settings and of the story-telling, this will transition smoothly into a full-fledged RPG campaign (perhaps diced, with character advancement if you so wish, and with a “central authority” such as a game master).