As another RWBY Fan (and I agree that volume 2 was not as good as volume 1, and we'll see what happens to volume 3) and long time GURPS fan, I must say that I feel that GURPS is not the right system for this. Sure, it can replicate the action on screen, but the problem is that the show is quite inconsistent and/or disregards physics a lot. Of course, if you went for a grittier feel, GURPS might suit you better.
For the over the top, fast and lose feeling that exudes from the show, however, I wold recommend
Fate Accelerated. Just to give you an example of why, with my rendition*
Yang Xiao Long's character sheet in FAE;
High Concept: The Hot-Headed Thrill-Seeking Brawler
Trouble: I Never Knew My Mother
Other Aspects:- Bearer of Ember Celica
- "You'll Never Make Me Bow"
- Rose's Protector
Approaches:- Good (+3): Forceful
- Fair (+2): Flashy, Quick
- Average (+1): Clever, Sneaky
- Mediocre (+0): Careful
Stunts
- Because I am more than meets the eye, I get +2 when I Forcefully attack when in a fight where I was hit strong enough (meaning that I took at least a mild consequence).
*This is a quick rendition, out of my head. It could certainly be improved
The beauty of FAE here is that it is so minimalist that it lets you distill the characters to their very essence, and that the fate point mechanic lets you do the crazy stunts shown in the show, without needing to have them permanently written down on the character sheet. Like many similar works, characters often show a single, one off ability that would solve future situations but they never use again. In FAE, it was an aspect invocation.
Aura is represented by stress and consequences, it doesn't need to be an explicit part of the system