If I play Falling Star, do I have to wait for my opponent to give no response, then I can use Stupefy afterwards? Or can I first use Falling Star, then hold priority and use Stupefy immediately?

You can play Stupefy immediately without waiting for the opponent. After your Falling Star becomes a Finalized Chain Item, you (as the controller of the newest item) gain Priority first (Rules 337.1.c.3, 312.2.c). Since Stupefy has [Reaction], it's legally timed during the Closed State, so you can play it right then before your opponent gets any chance to respond.

This is sometimes called "holding priority" — you can chain multiple spells together (in this case, your Action-spell Falling Star followed by your Reaction-spell Stupefy) before passing. Priority only passes to the opponent when you choose to pass (Rule 338.1.c), and you don't have to do that until you're done adding to the Chain.