I'm not fixated on any particular art style, but I do want to establish a distinctive look and feel that can be continued in future books in this series. The story is very much centered on the protagonist, and her struggle to find a place for herself in a lawless far-future setting that combines the themes of the traditional cyberpunk, space opera and military SF genres. Each book is going to focus on a different phase of her life, so I'm looking for a layout where some elements can remain the same while others change to reflect her changing circumstances.
Some details that might be useful for a representational style of cover art:
Alice Long, the protagonist of the story, is an innocent-looking fourteen year old girl with a slender build, long black hair, violet eyes and generally Japanese-American looking features. She generally favors feminine, 'girly' clothing, although there are some action scenes where she switches to an armored bodysuit. While she often carries a gun, it's usually a cute little pistol that's color-coordinated with her outfit. Partway through the story she acquires a pet dragon (actually a personal protection robot, but it looks like an animal) that's about the size of a housecat, and likes to perch on her shoulder.
Alice visits several planets during the story that provide very diverse background scenery - a jungle world, several Las Vegas-like spaceports, a Mars-like world, and a city-sized floating habitat on an ocean world. She also spends quite a bit of time inside space stations and on board a large space freighter. One of her more significant quirks is that she doesn't need a spacesuit, and is often found wandering around 'lethal' environments wearing a cute dress instead of protective clothing.
The setting defies the usual dystopian tropes, in that it assumes that the far future is incredibly rich in material terms compared to our present world. So everything looks shiny and new, with plentiful creature comforts and roomy interiors even aboard spaceships (which tend to be rather enormous).
Some hints and ideas for more abstract sorts of cover art:
Perilous Waif is the story of a young orphan girl leaving the primitive colony where she was raised, and setting out to find a place for herself in a strange universe full of exotic wonders. So images suggesting the vastness of space, the oddities of alien worlds or just travel and discovery in general might be useful design elements.
However, it's also an adventure story with a lot of fighting, and the future Alice lives in isn't a nice place. At first glance it looks like a bright, shining future full of space colonies, giant starships and wealthy people enjoying the fruits of medical immortality and advanced nanotechnology. But when you scratch the surface you find brutality and suffering on a massive scale. Colonies turn whole populations of androids or even humans into mind controlled slaves, fight genocidal wars over religion and ideology, and casually deploy nuclear weapons in every minor skirmish. Humanity struggles to adapt to technologies that have rendered traditional societies completely obsolete, with some colonies transforming themselves into something nonhuman while others retreat so far into their virtual amusements that they lose all contact with reality. So some suggestions of these darker themes would also be appropriate, as long as they don't dominate the composition.
The general mood of the story is upbeat, with the protagonist generally powering through obstacles with a combination of intelligence, determination and her personal enhancements (she's basically a genetically engineered supersoldier, hence the title of the book). Alice's journey of discovery takes her to some dark places, but she generally finds herself equal to every challenge and emerges victorious in the end.