I play Kayle from the jungle, and love her as a hybrid.
I often build:
Ionian boots
Infinity Edge
Nashor's Tooth
Rageblade
Gunblade
Guardian Angel
I like having the cdr to keep her e constantly up, turning her into a permanent ranged hybrid carry. Also, since you get focused I like picking up guardian angel which adds a lot more options for uses of your ult since you don't have to worry about yourself as much. This build is squishier, but she's made to stand back and destroy, and chase people, as well as saving whomever's being focused.