Reddit mentions of A Civil Campaign

I enjoyed starting them chronologically; it gives you a tremendous sense of the world-building and character-building she does over time, to see people become parents and their children grow up, and the references back to how things were - amazing stuff.

I'm going to provide Amazon.com links, but if you actually want to get these in e-book format I'd recommend going through Baen Books, her publisher. They really do e-books right - no DRM, e-ARC copies, free library - they're notorious for having some of the worst cover art in the publishing industry, too. Like, hysterically funny bad covers. (Shouldn't be a selling point but I like them better for it. They're one of the smaller "big" sci-fi publishers, with a snarky fun attitude.)

I'd go in this order, if you want to go internally chronological:

Shards of Honor

Barrayar

The Warrior's Apprentice

The Vor Game

Cetaganda

Brothers in Arms

Borders of Infinity


Mirror Dance

Memory

Komarr

A Civil Campaign

Diplomatic Immunity

Cryoburn


Fair warning - it starts strong and ends strong, but a couple of the middle books can feel a bit like heavy slogging. Totally worth it, in the end, though, since everything in this series ties together so tightly that when you've read the whole thing, it's a joy to behold how she put it all together.

There are also three major side-stories that take place in the same universe, containing characters which directly influence the main family tree or the history of the universe.

Falling Free - takes place long before the other stories, and makes good backstory to one of the odder races in the Vorkosigaverse. Not as readable as the others, though, so maybe leave it until later.

Ethan of Athos - easily the easiest read of the side stories; interesting, and mostly unrelated to the other plots. Just the author's take on a concept, really, taken to its logical extreme. She does flesh out one character that would, in most universes, be a throwaway. IT's nice.

Captain Vorpatil's Alliance - apparently a LOT of people insisted on finishing up a story for this guy. This one seems like pure fanservice to me, like she threw up her hands and said "Fine! Ok, all right already, here. Now leave me alone about him already." It's still very good - her idea of bad writing is what most people think of as their good writing - but it's a fluffy little bit of spytastic nonsense, mostly.

Komarr and its sequel A Civil Campaign by Lois McMaster Bujold

And then there's another sort-of-sequel focused on one of the side characters: Captain Vorpatril's Alliance