This reboot is specifically for an animated show I dreamed up that will never happen haha.
Barbara Gordon is a 17 year old High School student who is entering her Senior Year. Her father, Commission Jim Gordon is her idol and inspiration to become a police officer herself one day. Unfortunately Jim refuses to accept his daughter's goal and insists because of her genius intellect and gymnastics scholarships (which would allow her entry into high prestige schools) she should go to college and become a doctor or a lawyer or something outside of being a police officer.
Despite his protests, Barb insists on proving to her father and herself that she can do it.
The particulars, Batgirl ISN'T infatuated with Batman. Her choice of identity is because Jim trusts Batman despite not even knowing who he is, and she feels if she can prove herself behind the mask, then when she reveals herself to him he'll have to accept that she's a capable crime fighter.
Her costume is actually a couple of her gymnastics leotards refitted together in costume fashion. She raided her father's old locker in the basement finding one of his kevlar vests. She uses the internet to learn how work Kevlar into a fabric and lines the purple center mass of her costume with it.
The belt is mostly a stylistic choice for it's look, but it does contain various items like a utility belt, but as proven by the multitude of batman cartoons, reaching behind her back would serve as a 'tell' that she's gotten something out of her belt so no need for animated pouches.
Batman would rarely appear on my show. He's more a symbol than a character for Batgirl. Jim as well would likely only be seen from behind or through doors talking to her. I don't want him to be some overbearing figure, more he's a path and a Macguffin for episodes to overhear talking about cases she could solve.
Her nemesis in this would be Harley Quinn. A girl from her school who has similar aspirations, but is more localized on trying to get the notice of the Joker.
As the show goes on, each girl would be less inclined to try and prove themselves to some man and instead start realizing they have their own paths to follow independent of other's wishes or demands.
I think possibly Barb would find a semi-mentor in Catwoman rather than Batman. Catwoman would still be a cat burglar but her knowledge of how both Batman and the police work would give Batgirl insight and guidance. She'd of course continue to try and catch Catwoman but wouldn't succeed. Similar to Cassandra Cain's relationship with Lady Shiva. She's a bad guy, but has knowledge Barb can use.