In general, life in Skyrim is dangerous as hell, nowhere is safe. Whiterun is the best - home of the Companions, moderate climate, good view over the countryside so you can see the danger coming and plenty of single women.
My first thought was a cook, but then I remember that if you're a good cook (known in all of Skyrim) you get stabbed or robbed rather often by people trying to go undercover into parties. Being a baker would be nice though.
Blacksmithing might be nice, but in the end you lose your hearing and your body is under constant physical stress.
Lumberjack? What I did notice is a lot of lumber mills that are without any people working in them, that's kind of scary. Plus you most probably go to the woods and there are vampires and bears in there.
Priesthood offers some peace, but again safety is kind of the issue and there's all that need for praying etc.
Librarian also sounds nice, but people get greedy around books in Skyrim, plus how many of them are magical or cursed? One day you dust of and old book and the next you're a blind troll. No, thank you.
So maybe an apothecary. Not an alchemist mind you, those are the guys who's bodies you find in a deep cavern because they were trying to pick some mushrooms. I'd get my stuff brought in (there's always some stupid adventurer that needs money).