i think they could connect this show to Arrow and Flash and expand that universe nicely and created a good Earth-2 feel with the characters used. as for how to do her, would go with this being a world where Kara, not Kal-El, is the last survivor of Krypton and as a baby sent to Earth (basically making Kal-El the older cousin if there are ever Krypton flashbacks) and grew up as Linda Danvers. Would first have her appear in a Flash guest appearance in an episode where she's a high school senior from Leesburg in Central City on a field trip. She gets drawn into a conflict and has to openly use her powers for the first time (the conflict should be alien in origin and reveal her own origin that the Danvers never revealed). This leads to a conversation with Barry that sets her on the path to being a public hero in her own series. That kicks off as she starts freshman year at Metropolis University and her actions earn her the name Supergirl.
as for a costume, i think live action has proved the usual leg-less look is a bit silly (at least in my opinion) and i'd prefer they use her outfit from the Smallville Season 11 comic series. Not revealing but i think a cool, different look that fits better with the Arrow/Flash universe.