Miles Vorkosigan wants nothing more than to be a great military leader for the Barrayan Empire, like his father and grandfather before him. He would be amazing at it: he's brilliant, persuasive, inspiring, energetic, persistent... but he can't pass the physical tests to enter the academy. He's too short, and his bones are so brittle he could break them if he just tripped and fell. He's trying to prove his worth in a place where killing deformed babies at birth still hasn't quite gone out of style. His father's world isn't ready to accept him.
But he's his mother's son, too. Cordelia Naismith Vorkosigan was captain of a survey ship for the much more liberal Beta Colony, an explorer and a war hero against the Barrayaran Empire in which she now lives. She doesn't think very highly of the way Barrayar treats its weaker members of society: the poor, the handicapped, the women. "Barrayar eats its children," she says. She's a major player in dragging Barrayar out of its dark ages, and a role model for Miles (and the reader, IMO) in how people ought to treat each other, and how far you should be willing to go to bring that about.
Cordelia's Honor, with Cordelia as the point of view character, addresses women's issues directly: how does a woman who has power and status in her own liberal society adapt to a more feudal, military one, in which she is expected to have none? Cordelia never buckles - she never forgets that she is strong and does have the power to effect change, despite most Barrayarans' constant insistence otherwise. And Cordelia's the one who's right, even as she operates within the constraints Barrayar puts on her. In Shards of Honor (the first book in the omnibus), she's interacting with Barrayar as a soldier in a wartime situation; in Barrayar (the second), she now lives on Barrayar, where she's expected to be nothing more than wife and mother. But civil war breaks out, and Cordelia's motherhood becomes a battleground in the process. Barrayar addresses a lot of issues with pregnancy and the uterine replicators that replace it; recovering missing children; defending the children you have whether or not they're yours; and the power inherent in a mother's influence on her child.
Miles's books are less direct; in them, the appeal-for-reasons-of-being-female is more an issue of positive representation. Every one of Miles's love interests has a life of her own. They are not his sidekicks; they are not his prizes; their happy endings are different from Miles's. Many of them take one look at Barrayar's patriarchy and say Hell no; I won't follow you there. And Miles is a respectful, intelligent dude - he never once downplays their problems, never once tries to claim that Barrayar isn't a backwards little hellhole for women. But he can't abandon Barrayar, because he's trying to make it better.
This is my favorite series of books ever. I really can't recommend it highly enough.
You can read most of the series in e-book DRM-free,
Anyway, The Warrior's Apprentice is contained in the omnibus Young Miles. Cordelia's Honor is actually two books - Shards of Honor and Barrayar - but you can only get it in the omnibus these days.
You can buy them in e-book (any format) from Baen's store - full list of Vorkosigan titles here. It looks like you could log in again to re-download at any time, or in a different format. They've got something called "MicroPay" which looks like store credit - I didn't play with that.
Also: there's a new book in the series coming out in November! It's about Ivan-you-idiot! I'm excited. Do you think he'll finally get involved in a long-term relationship? I've been looking forward to that since A Civil Campaign. I kind of hope he marries a girl just like his mother. It would be hilarious.