"Whats the best style for quick and powerful self defense?"
There is only one correct answer: The style you have practiced hard and learned well.

And then person woke-up...quick seemed to me to indicatate a person with at least virtually no training to acquire powerful "self-defense". If it is not study time oriented then of courseyou are not wrong~

Kara-te--you can learn techniques quickly that are powerful~ within a month.

Aikido/Juijitsu (not the stuff called Brazilian)/Bujinkan(taijitsu)--can learn powerful self-defense quickly~

I'm not sure how Wing Chun begins but the stance and hands indicate that this would be powerful self-defense learned quickly.

Praying mantis, if the do forms first would be good but might be too techniquey to be a quick learn to get powerful techniques.

Shaolin and the other fighing Kung-fus are too develope the body first to learn powerful sel-f defense quickly.

Arnis type things would be good except weapons arenot all the time on hand, even sticks. So I'm sticking to empty-hand thingies.

Interenal arts--take a month to begin to get propper strength and years to get useable real fight comprehension...

If what was meant was styles~that even after long use gets one quickness and power for "self- defense", then Jerry Love at least as basically correct. They all can be some kind of good. While they have their own -nesses the individual can mold it to accentuate the aspect(s) of choice. Note:this use by preference alters that art from it's way to be passed on. Pass it on the way you're taught~ make it your own~. Shw them your way after you've given them The Way. Then they can find Their Way. Which like children is a littlebit of you and a little bit of your teachers, anf a little bit of their teachers...Perhaps, some-such.

Very some such,perhaps might have been, likely say some, some not.