I'm torn between option 2 and 3. Having a set cycle is nice because if you want to interact with that character there's no possibility of not getting that person.
However, having a little bit of controlled randomness gives just a little bit of personality to these characters. It provides the perception that these characters have things going on in their lives that effect when they go do things.
If I have to make a choice I would go with option 2 because it's less work and I can get to the fun stuff quicker.