I like to get about halfway into the career with a single sim, and then I may have them move in with a significant other. They might start a family and during that time, I work on getting their promotions until they max out. They stay in that job unless I believe it's in their character to switch paths.
As for skills, I do that simultaneously and develop skills that are related to their chosen career or what I feel fits their personality. When they get to the max level of their career I don't necessarily get bored with them because it just means I have more time to focus on their partner's career/interests or kids (and their personal lives, making friends, finding potential partners for their future, building their skills too.)
One time I wanted to add something new to my sim's story because they were just a little too "perfect" and their record was too "clean"... in my head I made them have a scandal where there might have been rumors that they had to woohoo their way to the top (and maybe it could've been real?) and I made them lose their job and they needed to start from square one. The possibilities included starting in perhaps a different career, having to rebuild their image, move worlds...
All in all, I generally leave them be when they've made it to the top, but again, if their life is too great I definitely want to turn it around :) Because we love having sims suffer from time to time, right? Right.