The Price of the Stars by Debra Doyle and James MacDonald.
Beka Rosselin-Metadi, daughter of the leader of a world that was destroyed in the Mage Wars and the general who led the fight against the Mages, works on trader ship. On one port call, her father's aide calls her to a meeting with her father, who happens to be in the same port.
He tells her that her mother was assassinated and offers her his spaceship, the Warhammer, in exchange for finding out who killed her mother.
Beka left her family because she didn't want to be the Little Domina, her mother's heir apparent. She wanted to be independent, anonymous, free of her familial ties. She takes the ship, regardless of price.
Her quest to root out the conspiracy behind her mother's murder takes her to many worlds, where she joins up with her brother, an Adept (like a Mage, but not evil), a friend of her brother's, and a mysterious man she nicknames the Professor, who claims she was her family's servant on destroyed Entibor.
The conspiracy is rather deeper and twistier than they expected, with tendrils leading to surprising ends. There are two direct sequels, a couple prequels, and a next generation book, all of which I'm hoping to read.
It's a fun tale, with a lot of space ships and explosions and dry wit. It's Star Wars-esque, but that isn't necessarily a bad thing: for one, the dialogue is better and the characters a bit more well-rounded in this book. If you like space opera, you will probably enjoy this book.