For me, it's most important to start attempting by turn 2. There are a lot of dilemmas you don't pass with your personnel, you just trigger them and wait for some other condition in order to pass:
Experience Bij,
Dead End,
Edo Probe,
Whale Probe, most
,
Friendly Fire (after
Personal Duty). That, plus other countdown dilemmas, and the value of gathering information, are why I like to start attempting early.
So on turn 2, I'll send almost everyone at a mission, protecting any personnel needed for plays/draws, and often protecting an extra
so that I don't get stuck unable to staff ships.
For early and mid-game attempts, I run down a short list of dilemmas that represent the worst things that are likely to happen. If I can reasonably play around those dilemmas, I will; otherwise I just hope for the best. So, for a while, I would form an Away Team and crew that could pass both
"God" and
Jol Yichu if I could with my available personnel. Typically I try to have 2 personnel with MEDICAL for
Hippocratic Oath +
Plague Ship. I usually don't care too much about point loss dilemmas until I know that they are a part of my opponent's strategy.
Late game attempts, when I have a ton of personnel but need to solve this turn, is an area where I could use improvement.
Against
The Squire's Rules, I pretty much just send everyone, though I may consider if I want to limit point loss from
The Higher... The Fewer (usually I don't care). The random dilemmas and random stops mean that it's not worth it to try to play around particular dilemmas, and the fact that they're all Either dilemmas means that not many terrible things can happen. I find The Squire's Rules to be less fun to play against for these reasons.