Of the professions, I'd say Private Investigator. The reason is you don't have to spend long hours away from home all day, and there is nothing to repair or alter in your neighborhood.
What I don't like about Firefighter: Constantly maintaining the firetruck and alarm. Your fellow firefighters spend 20 hours per day at the station--they don't have home lives. You can't invite them over or on group outings because they're always on the job. Also, once there's been a fire at someone's house, the burned and charred marks stay in the house and on the property forever, lowering environmental score if you ever go to their house later when visiting. It looks dirty and Sims don't like it.
Stylist: With Edit in CAS, if you don't like the way a Sim looks around town, just fix them up with this feature anywhere, anyplace. It takes only moments of your time, and your Sim can still enjoy any other job you please. You don't need Stylist career.
Architect/Designer: It's fun at first, but begins to be monotonous. It also greatly increases the size of your save files because of all the permanent changes you are making to properties around town. It is a long work day, 8am to 6pm 5 days/week, and the rest of the time you need to constantly paint, or create hand-crafted items, with hardly no social life.
Ghost Hunter is pretty cool and fun, but be prepared to always work the graveyard shift and sleep all day when other Sims are out and about. It also becomes monotonous after a while.
In contrast, I prefer regular careers or the work at home careers, like Inventor, Sculptor, Painter, Writer, Gardener, etc. Even Fishing or Photography career is nice and gets you out of the house whenever you choose at your leisure, and lets you meet Sims and socialize along the way. There are really nice monetary and other awards in all these skill-based careers as well, besides the fact that your Sim sets their own hours.