Bujold's own preferred path: internal chronological order, not publication order. Start with the parents' story before their son takes the series entirely over.
Shards of Honor
Lois McMaster Bujold
Barrayar
The Warrior's Apprentice
The Vor Game
Cetaganda
Brothers in Arms
Mirror Dance
Memory
Komarr
A Civil Campaign
Diplomatic Immunity
CryoBurn
Gentleman Jole and the Red Queen