There are very few styles I would coin as unorthodox. Aikido and (Shaolin) Kung Fu being most principle in my mind among them. Since Kung Fu doesn't interest you, and Aikido does lack a lot of useable techniques, I personally don't see things like Karate as unorthodox because Karate in general is an Art that is fairly direct and to the point; I don't use the stance being right leg back or right leg forawrd to determine the orthodoxy of a Martial Art or style. There are few aspects of a kata I would consider useless, that is not so true for some unorthodox styles.
I humble suggestion: You'll learn whatever you feel best. Look around a bit on the internet and in reality, go visit the schools from any Art that peaked your on-line interest and see if it still draws your attention when you see live bodes practicing it. If you like it, find it effective and worth it, go for it.
Sig courtesy of that photo-matic magician limba
I went out the way that I fight. I went out on my shield. That’s it. Done. --Chuck Liddell
My goal is to end my opponent --Carlos Condit