You'll probably get a few different views on this one NF. The first story chronologically is Falling Free, but whilst this is set in the same universe it is not really a Vorkosigan story, though the 'quaddies' from that story do make a reappearance a couple of times.
Again chronologically, this is followed by Shards of Honor and Barrayar (available together as an omnibus). These are actually about the parents of Miles Vorkosigan and is frankly a little heavy on the romance side for my taste. Some like them, some say skip them, either way there is no denying there is important back story in them and they are a pretty quick read as I recall.
After that is the first of the true Miles Vorkosigan stories - Warrior's Apprentice - which on my rankings is the best of the series to that point. Some say start here but my earlier warning about back story stands.
Additionally you have to realise that at least one of the books that follows this - Ethan of Athos (about 3 books farther on) - is again not really about Miles but is a bit of a side shoot story. I don't know if there are others like that, but it's not a bad story and addresses an interesting idea quite sympathetically.
I have got a timeline that identifies where the various books and short stories fall, if you would like a copy (PDF).