I do the lingering damage health and a regular damage health to make sure they die, I'm far away by the time they die and don't get caught. Now that I think about it, a frenzy poison in a crowd might be funner....

Wait till night, firstly. The target will either be asleep or at least be much more likely to be alone. And at night you have a much better chance of being undetected. Also i would use dual daggers instead of a bow for assassinating. Even without the dagger sneak attack perks it is much more reliable to kill someone quickly with 2 sneak attacking daggers than a bow.

For killing people in public I just stick a frenzy potion in their pocket. They go nuts, then get killed and no one suspects me.