Someone over at MATY said that the only traits that affect career progress are brave for law enforcement and evil for criminal; and ambitious for all careers. Also, the multitask reward increases the rate you progress.
Natural cook and other skill-traits don't increase the speed of progress directly, but you will be able to get cooking faster, which indirectly leads to promotion. Also, workaholic just makes you lose less fun, gives a nice moodlet while at work, and makes your Sim autonomously work hard.