With respect to female characters, the one I find most entertaining is Captain Sarah Essen. I think the actress's comedic skills aids in my appreciation.
My knowledge of Batman lore is severely limited. The earlier episodic episodes weren't doing much for me, but the last two have been really good. Kinda loved this past one. I can't remember the last straight-arrow character being so compelling as Gordon. Maybe Nikita, but her past was shady so there was a redemption aspect to that character.