I've had Syrian hamsters ever since I can remember. And I rarely had a Syrian bite me. My first hamster bit me and my mom, but she was a female, and I was fairly young so I wasn't handling her properly. Anytime after that, I can stick my hamster's heads in my mouth, let them crawl all over my face, and they don't even think to bite. My second hamster, which came about a couple years after my first died, developed arthritis, and we could sleep in my lap while we all watched Star Trek. My third got a stroke, and my dad....well....he ended his suffering, because he lost mobility of his hindquarters and had to drag his back half around.
My fourth died of old age, my fifth died from Wet Tail, my sixth killed herself(Dwarf. I don't trust y 'em), and my seventh, eighth and ninth died from old age, my tenth froze to death(faulty furnace, it had to be physically booted to work, it wouldn't even kick on automatically if it was below freezing in the house), my eleventh, and twelfth died from old age, and my thirteenth... I think he caused himself internal bleeding, and that's how he died.
Anyways, in listing all my hamsters through the years, despite their medical or physical ailment, and not including the first, they NEVER bit me.
I prefer males. In my experience, females smell. Any time I had a female hamster, I would get this stench on my hands and clothing. Males I never had that problem. But both can be equally calm and serene. Like I said.... I've put their heads in my mouth, accidentally dropped them, and through everything, they never bit me. But then, I handled mine at least 2- 3 times a day.