Batgirl. For me it all depends on which iteration of the character we are talking about. Especially with a character like Batgirl where there have been several different ladies who have been this character, each one bringing an interesting twist to the character.
I'm with this guy. All of them have their good points, very good points in fact. (And that was not a joke about any parts of their anatomy.)
I've never read much Zatanna. I used have a big thing for Black Canary back when I was in university, and then there was Starfire and Katana hanging about. Not sure about the latest incarnation of the last of those, but this was back when Batman and the Outsiders was running and Katana used to threaten people in the letters column with having to carry their lungs home in a bucket. Being threatened by a fictional character was a badge of honour. Ah... those were the days.
Also, I don't have kids, but this is like picking a favourite out of my characters. I guess that's usually the one I'm writing, so... last comic I read with a female lead was the Wonder Woman: Rebirth one so Diana gets the vote. Close call, could have been Babs or Harley if I'd read them in a different order.
Hmm...even then that's pretty tough. That probably narrows it down to Wonder Woman and Barbara, but I guess that depends on what kind of smarts you're looking for? Diana is expertly trained by the amazons in combat and knows a lot about diplomacy and philosophy. Meanwhile, Barbara has an eidetic memory and is an expert on science and technology.