When you play an effect that targets a character or location do you have to target the character or location before your opponent gets the chance to cancel?

For example

I bring a black cells out of shadows, do I have to announce the character I want to target first, then my opponent chooses to cancel. Or does my opponent have to cancel it first before I choose?

When you play an effect that targets a character or location do you have to target the character or location before your opponent gets the chance to cancel?

For example

I bring a black cells out of shadows, do I have to announce the character I want to target first, then my opponent chooses to cancel. Or does my opponent have to cancel it first before I choose?

Yep. Choosing applicable targets for an effect is done before the Save/Cancel response step.

You have to choose first.

A cancel interrupts the initiation and resolution of an effect. The initiation is complete and done before the cancel can be played (that's why canceling doesn't "refund" any costs that are paid). Choosing targets is part of initiation, and so must be done before any cancels can be played.