Adam Koebel, in a video somewhere (early on in Roll20 Burning Wheel, I think), suggests you make your three beliefs be, in turn:
- About your past life
- About your current situation
- About another PC — how you relate to them
In StarCruiser, my main advice is that they should collectively be:
- Resolveable in the space of the current arc
- Things that will involve your PC with other PCs (even if only indirectly)
- About things that you, the player, want to see in play
Paul Beakley, over on G+, presents his Best Practices for BW Beliefs (and Instincts, and Traits). They include a list of what your Beliefs and Instincts should cover:
1 Belief or Instinct about the GM’s situation. Usually the GM will pitch the game around one or more core things. Think Fronts from Apocalypse World.
1 Belief or Instinct about another PC.
1 Belief about something in the setting that interests you personally. Your flag to the GM that says “I’m really interested in this thing.” Yes, just a Belief, not an Instinct in this case.
1 Belief or Instinct that’s just totally wrong. Like, you’re just straight up mistaken or incorrect about something.
1 Belief or Instinct that contradicts another of your BITs in some way.
Another thing he says which seems valuable:
You also want to make sure you have about a 50/50 division between internal and external tensions. If it’s all external, you have a very traditional “party” and that’s boring. If it’s all internal, it gets really fraught really fast. Hard for long-term play.
The Burning Wheel Codex (print only, $35 US) has further long-form advice on this and many other topics (although the bulk of the ~600 pages are taken up with BW-specific stuff, and based on a quick comparison most of it was also in the old Adventure Burner). Pleasingly, the main chapter on Beliefs is available as a free sample (it’s the older version, but I don’t think much has changed).