Good question. I didn't follow the recommended reading order on either list exactly. "Warrior's Apprentice" is a great place to start to get introduced to Miles and the setting and the author, to see if you really want to invest in the series. Then, going back in time to get the Vorkosigian / Barrayar backstory is wonderful ("Shards of Honor" followed by "Barrayar"). I'd then just pick up the internal (i.e. storyline) chronology following "Warrior's Apprentice", as there are references to earlier events in the earlier stories.
Although the novel "Falling Free" is the earliest in the internal chronology, it has very little to nothing to do with the later novels. It is a great yarn nonetheless. I'd read it when you want to understand more about the history of the quaddies.
Hope you enjoy the series as much as I did. Great stuff!