*Exiting lurker status to show support for Kara.*
Even though Superman is quite the role model in my own life, I've found Supergirl to be more often relatable. She may be more of an alien than Superman, but I think being thrust into a strange world with no home or family to go back to gives her the opportunity to feel more human than Clark. Suddenly being different to everyone around you vs. growing up different.
While I agree that this new Superman needs to be well established on his own with a few movies, I think she would best fit in when she’s needed or where she'd support the main storyline. Aside from being a super powered helping hand against a massive threat; her Kryptonian knowledge could prove a necessity given the situation.
For her costume on Earth, I’d love to see everything identical to Superman’s... minus pants.
To complete her iconic look and be somewhat original, she would tear the bottom 1/4th of her long red cape off and attach it to her belt, fashioning a makeshift skirt. I think the only thing safe to assume so far about Kryptonian under-armor uniforms, is that they’re the only clothing available that won’t be destroyed during super heroics.