I think following a challenge is the easiest way to find a red thread. Why don't you just read through a few of them. May be you get an idea while reading. If not try not to force a plot. I'm not a sims-story-writer but I did wrote some original stories even if I'm a bit rusty right now.
You don't have to follow certain rules, you can bend them like you want to bend them.
And fanfiction isn't equal to shipping people :D It's quite common but it works brilliant without random pairings. May be it could be really interesting to focus on other things than love relationships.