I quite like idea of a separate story mode, something akin to The Journey in FIFA, or the story focused single player campaign you get in most E.A sport titles, such as Madden, NBA etc...
You would start as a rookie in a lower formula, perhaps immediately meeting your flash, arrogant nemesis and battling him on track.
Your personal decisions would dictate your progression, not the pre set, unalterable game developers choices...and each player could see multiple endings.
As long as it wasn't too schmaltzy and cliché, and allowed a genuine sense of pride in your character, and was paced correctly, with the speed of advancement to F1 based on your ability, but also recognising that you can pick the wrong team, come up too early and fail, or waste an opportunity and see it go to another driver.
If it was done well it would be such a fantastic experience.
Naturally the more traditional modes, such as single race, time trial, online etc... would be standard.