The first question is why would I pick her?
Normally she doesn't have the axe, but by the end of this I hope you'll understand that she doesn't need the axe to kick ass. First off, she was part of the Justice League, Birds of Prey, and was an elite warrior from her home planet, for further reference, watch this video in which she kills her former subordinates.
Here it is.
It wouldn't let me put it here so there's the link.
It should be noted as well that Wonder Woman is awesome in this, and in other things as well. But Wonder Woman gets plenty of attention, so I'm giving Barda a second in the spotlight. Of course its not a great spot light, but better than nothing. Anyways, one of the reasons I admire Barda is that she has actual armor. The first time I saw her its what won me over. It was in this episode of Justice League Unlimited that she was brought to my attention. Of course she does have some fantasy moments.
Keep in mind she could still end you.
She's also married, to Mr. Miracle (Scott Free). Which points me to my next point, they were a gender reversal in who's stronger and protective. She is the powerhouse in the relationship, and although poked fun at sometimes, she still has moments of just wanting to be a normal person. In the 80s comic, she wants the neighbors to not think of her as a freak at times. And the relationship isn't some attempted love triangle, or one that people aren't sure if it really works, they love and respect each other. Every time Mr. Miracle shows up, Barda at least has some face time, and they'll joke with each other. And this is one of the two comics of Mr. Miracle I owned.
I enjoyed the partially humorous nature of their relationship. Its in someways ridiculous that she is the "man" in the relationship, but it really works for them, so what does it matter?
Like most comic book characters, she's evolved over the years and all for the better. She's still stayed strong, but stays pretty much true to herself.