I've seen Miles before (not counting his time as a fetus and small child in Barrayar) in "The Mountains of Mourning". As a short story set in a very fleshed-out universe, "Mountains" didn't give me too much to go on about Miles, except for his odd relationship to his people - as a mutant, as a half-foreigner, as a lord... 
 Apprentice didn't give me too much more to go on in understanding his relationships with his family members (Aral gets about as much page time here as he did in "Mountains"), but I did get to see a lot more of Miles himself. Much of the book is spent off-world, which was an interesting contrast to "Mountains" as it gave me a glimpse into how Miles is Barrayaran, as opposed to how he is not. 
 A big focus of the story is on his relationship with Bothari. In fact, Bothari's been fairly central to all three of the books I've read so far, with Escobar as the linchpin to many of the central events in all three. Miles's relationship with Bothari is, of course, very different from Aral's or Cordelia's, and that added an interesting dynamic. 
 Mostly, though, this book is funny. Bujold is great at this deadpan absurdism - in this case as Miles accidentally builds an army. Throughout the first 2/3rds of the book, Miles just goes from situation to situation, snowballing his successes well beyond what he's able to handle. It's like the Chosen One trope, but self-aware.