For spells that deal damage or modify stats, when must targets be chosen - immediately when cast or after other cards can be chained?

Ruling: You must choose targets as you put the spell on the chain, before anyone can react.

Nuances:

• This does not apply if the spell says "Do this" (non-reflexive). In that case, you don't target when casting - the spell resolves and puts instances on the chain that require targets when those instances are added.
• Example: Falling Star says "Do this twice: Deal 3 to a unit" - you don't target when casting, but when it resolves it puts two "Deal 3 damage" instances on the chain and each instance needs a target at that point.