Vatta's War series
1 Trading in Danger
2 Marque and Reprisal
3 Engaging the Enemy
4 Command Decision
5 Victory Conditions
These 5 books are not so much a series as one long novel - there's one story arc, and you really need to read all five to get to the (satisfying) conclusion. (I somehow had the misapprehension that there were only 4 in the series - luckily the public library came through and got me #5 expediently!)
Due to a misjudgement, Kylara Vatta, scion of an interstellar shipping business, gets kicked out of military academy shortly before graduation. She's pretty crushed by the end of her hopes for a military career, but there's always the family business to fall back on... or is there? Someone's apparently got it out for her family, and before Ky knows it, she's catapulted into the midst of a space war, seeking justice and vengeance against an unsavory alliance of pirates.
These are first and foremost action-adventure books, with plenty of shoot-em-up scenes and an uncomplicated moral compass - you know who the 'bad guys' are, and although Ky is normally affected by the trauma of war (even seeking therapy at one point), she's always clearly on the side of right. The one thing I wished the story had was more exploration of the bad guys' motivations - OK, we know they're racist, and bigoted against 'modified' humans (people who've had either genetic or physical/technological augmentation), and of course they want power - but what's the story behind it all?
However, the characters of the 'good guys' are well-drawn, and the story's definitely recommended for those who like strong female characters: there's Ky, with her military and strategic brilliance, her cousin Stella, who has the financial and business acumen to bring Vatta Enterprises back from the brink - and there's their grandmother, Grace, who is far from being the harmless old lady people might assume. (Grace might be my favorite character - it's wonderful to see an older woman portrayed with such verve.)
As many have mentioned, there are some definite parallells here with Lois McMaster Bujold's Vorkosigan saga. I'm not sure these are *quite* as good, but if you like one, I'd guess you'll like the other.