Supergirl to an extent even before Crisis on Infinite Earths made it trendy often went through a lot of re-inventions. She was an orphan who operated in secret as Superman’s secret weapon, Linda Danvers, the post crisis version that wasn’t even an actual Krptonian, the post-crisis one who WAS Superman’s cousin again, the new 52 version, Rebirth, not to mention the TV show which has borrowed from several but is not truly an adaption of one particular era of Supergirl.
So… which is everyone’s favorite? Seems a good question to ask on this her 60th Anniversary.
Personally I can’t help but like the Matrix, Peter David era Supergirl. She may have been the one who was never truly related to Superman, and who had the most different powers (although once she got the Peter David book they did take away a lot of the powers that made her the least like a Kryptonian). I think Peter David did some of his best work on Supergirl, and while some more recent ones have done the character justice, none have truly been as interesting a character to me as that one.