What mattered in battlecruiser-versus-battlecruiser design?

What thought went into battlecruisers fighting battlecruisers, including the dangers of inadequate armour or speed?

The recurring aim was to gain more speed, larger guns, and longer range than the opposing battlecruiser.

Asked how navies approached battlecruiser-on-battlecruiser combat, the recurring answer is comparative advantage. A navy wanted its own ships to carry more speed, larger guns, and greater range than the opponent. The brief reply captures why requirements could escalate as rivals responded to one another. These preferences did not solve the armour trade-off raised in the question.