Do not look for a specific style. What matters is the qualiy of training you receive, and that is decided by the individual school and instructor, not the style.

Every martial art is applicable and practical for actual self defense. The best possible thing you can do is look into the martial arts schools and locations in your area and train at the best one. What matters is how good the school and instructor is and how you train, not they style.

And no, the thing you described does not sound like a certain martial art. Good luck with your decision.

Now go forth, and choose wisely.

Wing Chun

First off the best advice I can give you is to ignore Keyboard Warrior.

Secondly, find a Krav Maga training center near you and check it out for yourself.

KravMagaAlliance.com/affiliates

Taewando, maybe. I am not too sure because I don't normally take self defense classes and I'm more interested in Performing Arts

I've tried out traditional Karate and I didn't really like it but I'm still open to learning martial arts. I'm looking for one that could be used in a street fight but one that also teaches self defence and kicking with legs. Does that sound like a certain martial art?