When I play Rebuttal, do I have to decide to pay 1 more power to take control of the spell, or will I wait until it resolves?

You decide when Rebuttal resolves, not when you play it.

When you finalize Rebuttal, you only choose the target spell. The "You may pay [A]" isn't an additional cost of playing Rebuttal — it's a cost within an instruction, paid on resolution (Rule 204.3.b). So you play Rebuttal for its printed [1][P], and only when it resolves do you choose whether to pay [A]: pay it and you take control and may make new choices, or decline and it counters the spell.

One catch: the target must still be on the chain when Rebuttal resolves. If something else removes or counters it first, Rebuttal fizzles and you never get the chance to pay — you just keep your runes.